Q: Syllogistic inference about carpeting and color: All offices on the 9th floor have wall-to-wall carpeting, and no wall-to-wall carpeting is pink; decide whether the conclusion "None of the 9th-floor offices has pink wall-to-wall carpeting" must foll…

Given data Premise 1: All 9th-floor offices have wall-to-wall carpeting. Premise 2: No wall-to-wall carpeting is pink. Conclusion to test: No 9th-floor office has pink wall-to-wall carpeting. Concept / Approach Use categorical logic: If all items in Group A have Property C, and nothing with Property C can be pink, then nothing in Group A has pink carpeting. Step-by-step reasoning Step 1: Every 9th-floor office ∈ {carpeted}.Step 2: {carpeted} ∩ {pink} = ∅ (by Premise 2, carpets cannot be pink).Step 3: Therefore, for any 9th-floor office, "pink wall-to-wall carpeting" is impossible. Verification / Alternative view Contrapositive thinking: If an office had pink wall-to-wall carpeting, then there would exist pink wall-to-wall carpeting, contradicting Premise 2. Common pitfalls Assuming some 9th-floor offices might lack carpets; Premise 1 rules that out. Final Answer Definitely true.

Question 1

Logic consistency check on comparative ages: given 'Tanya is older than Eric' and 'Cliff is older than Tanya', evaluate the truth of 'Eric is older than Cliff'

Accepted Answer

Given data T > E (Tanya older than Eric) C > T (Cliff older than Tanya) Concept/Approach (why this method) Use transitivity of the 'older than' relation: if C > T and T > E then C > E. Step-by-Step deduction 1) From C > T and T > E, conclude C > E.2) Statement to test says E > C, which directly contradicts C > E. Verification/Alternative No equalities allowed by 'older than'; contradiction is decisive. Common pitfalls Reversing the order or assuming non-transitive relations. Final Answer False

Question 2

Transitive price comparison reasoning: given 'Blueberries cost more than strawberries' and 'Blueberries cost less than raspberries', determine whether 'Raspberries cost more than strawberries and blueberries' is true

Accepted Answer

Given data B > S (Blueberries > Strawberries) R > B (since Blueberries < Raspberries) Concept/Approach (why this method) Apply order transitivity on 'cost more than': if R > B and B > S, then R > S and R > B. Step-by-Step deduction 1) From B > S and R > B, infer R > S.2) We already have R > B; combine to yield 'R > S and R > B'. Verification/Alternative Construct sample numbers (S=1, B=2, R=3) → statement holds. Common pitfalls Assuming 'and' requires extra information—here transitivity suffices. Final Answer True

Question 3

Syllogism validation with set inclusion: if all trees in the park are flowering and some trees are dogwoods, assess the claim 'All dogwoods in the park are flowering trees'

Accepted Answer

Given data All Trees_in_park ⊆ Flowering. Some Trees_in_park ∩ Dogwoods ≠ ∅. Concept/Approach (why this method) Universal inclusion: every member of the 'trees in the park' set is flowering; any subclass (e.g., dogwoods in the park) inherits this property. Step-by-Step deduction 1) Let D = {dogwoods in the park}. By premise, D ⊆ Trees_in_park.2) Since Trees_in_park ⊆ Flowering, transitivity gives D ⊆ Flowering. Verification/Alternative Venn diagram: place 'Trees' circle fully inside 'Flowering'; 'Dogwoods in park' is a sub-region within 'Trees', hence also inside 'Flowering'. Common pitfalls Confusing 'some trees are dogwoods' with 'some dogwoods are flowering'—here all park trees are flowering, so all park dogwoods are flowering. Final Answer True

Question 4

Speed ranking logic: given 'Mara runs faster than Gail' and 'Lily runs faster than Mara', evaluate the truth of 'Gail runs faster than Lily'

Accepted Answer

Given data M > G (Mara faster than Gail) L > M (Lily faster than Mara) Concept/Approach (why this method) Use strict order transitivity on 'faster than': L > M > G ⇒ L > G. Step-by-Step deduction 1) From L > M and M > G, deduce L > G.2) The statement claims G > L, which contradicts L > G. Verification/Alternative No equalities or ties are stated; 'faster than' is strict, so contradiction stands. Common pitfalls Overlooking transitivity; assuming cyclical speed relations (not possible under strict 'faster than'). Final Answer False

Question 5

Relative apartment pricing logic: with Riverdale < Gaslight Commons and Livingston Gate > Gaslight Commons, determine whether 'Livingston Gate costs the most among the three' is correct

Accepted Answer

Given data R < G (Riverdale cheaper than Gaslight Commons) L > G (Livingston Gate pricier than Gaslight Commons) Concept/Approach (why this method) Order chaining: if L > G and G > R, then L > G and L > R → L is the most expensive of the three. Step-by-Step deduction 1) From R < G, we have G > R.2) Combine with L > G ⇒ L > G and L > R.3) Therefore, Livingston Gate is the costliest among {R, G, L}. Verification/Alternative Plug sample numbers (R=10, G=15, L=20) → statement holds. Common pitfalls Thinking we need a direct L vs. R statement; it is implied via transitivity. Final Answer True

Question 6

Mall size comparison logic: given 'Kingston has more stores than the Galleria' and 'Four Corners has fewer stores than the Galleria', evaluate 'Kingston has more stores than Four Corners'

Accepted Answer

Given data K > G (Kingston > Galleria) F < G (Four Corners < Galleria) Concept/Approach (why this method) Transitivity on inequalities: if K > G and G > F, then K > F. Step-by-Step deduction 1) From F < G, infer G > F.2) With K > G, chain to get K > F. Verification/Alternative Example counts (K=120, G=100, F=80) satisfy all statements and confirm the conclusion. Common pitfalls Assuming we need exact store counts; ordinal relations suffice. Final Answer True

Question 7

Logical reasoning (premises-to-conclusion): All the tulips in Zoe's garden are white; all the pansies in Zoe's garden are yellow; determine whether the concluding statement—"All the flowers in Zoe's garden are either white or yellow"—must be true ba…

Accepted Answer

Given data Premise 1: All tulips in Zoe's garden are white. Premise 2: All pansies in Zoe's garden are yellow. Candidate conclusion: All flowers in Zoe's garden are either white or yellow. Concept / Approach We are testing whether the conclusion is logically entailed by the premises (i.e., must be true if the premises are true), not whether it could happen to be true in Zoe's actual garden.Premises mention only two categories (tulips, pansies) and their colors; they say nothing about any other flowers that might also be in the garden. Step-by-step reasoning Step 1: From Premise 1, every tulip is white. This restricts tulips to the set {white}.Step 2: From Premise 2, every pansy is yellow. This restricts pansies to the set {yellow}.Step 3: The premises do not claim that tulips and pansies are the only flowers in the garden; other kinds (e.g., roses, lilies) may exist.Step 4: If other flower types exist, they could be red, pink, purple, etc. Therefore, it does not logically follow that all flowers are either white or yellow.Step 5: Because the existence and colors of other flower types are unspecified, the conclusion is not guaranteed. Verification / Alternative view Construct a countermodel: Suppose Zoe also grows red roses. Premises 1 and 2 remain true, but then not all flowers are white or yellow. Hence the conclusion does not necessarily follow. Common pitfalls Assuming that only tulips and pansies exist because they were the only types mentioned. Confusing "could be true" with "must be true." Logical entailment requires necessity, not possibility. Final Answer Cannot be determined from the given premises—the conclusion is not logically entailed.

Question 8

Comparative reasoning about quantities watched: Josh saw more movies than Stephen, and Stephen saw fewer movies than Darren; decide, strictly from these two premises, whether the statement "Darren saw more movies than Josh" must be true.

Accepted Answer

Given data Premise 1: Josh > Stephen (Josh saw more movies than Stephen). Premise 2: Darren > Stephen (Stephen saw fewer than Darren). Claim to test: Darren > Josh. Concept / Approach Translate the sentences into inequalities and then compare what is known and unknown.Knowing that both Josh and Darren exceed Stephen does not, by itself, order Josh and Darren relative to each other. Step-by-step reasoning Step 1: From Premise 1, J > S.Step 2: From Premise 2, D > S.Step 3: There is no premise comparing J and D directly. Both could be greater than S, but either one could be larger.Step 4: Construct models: (a) J=12, S=10, D=15 ⇒ D > J (claim true). (b) J=16, S=10, D=15 ⇒ J > D (claim false). Since both are compatible with the premises, the claim is not entailed. Verification / Alternative view Because two different consistent assignments yield opposite truth values for the claim, the truth of the claim is undetermined from the premises. Common pitfalls Assuming transitivity via Stephen (e.g., "greater than Stephen" implies a chain between Josh and Darren). It does not. Confusing "possible" with "necessary." Final Answer Cannot be determined from the given premises.

Question 9

Weight-ordering logic: Rover weighs less than Fido, and Rover weighs more than Boomer; determine whether the conclusion "Of the three dogs, Boomer weighs the least" must logically follow from the two given premises.

Accepted Answer

Given data Premise 1: Rover < Fido. Premise 2: Rover > Boomer. Claim: Boomer is the lightest of the three (i.e., Boomer < Rover and Boomer < Fido). Concept / Approach Chain the inequalities to find a strict ordering. Step-by-step reasoning Step 1: From Premise 2, Boomer < Rover.Step 2: From Premise 1, Rover < Fido.Step 3: Combine the two: Boomer < Rover < Fido. This establishes a strict ascending order of weights.Step 4: Therefore Boomer is lighter than Rover and also lighter than Fido, so Boomer is the least. Verification / Alternative view Any numeric assignment respecting the premises (e.g., Boomer=10, Rover=12, Fido=14) makes the conclusion true. There is no counterexample consistent with the premises. Common pitfalls Overthinking ties: the strict inequalities ("less than", "more than") already exclude equality. Final Answer Definitely true.

Question 10

Syllogistic inference about carpeting and color: All offices on the 9th floor have wall-to-wall carpeting, and no wall-to-wall carpeting is pink; decide whether the conclusion "None of the 9th-floor offices has pink wall-to-wall carpeting" must foll…

Accepted Answer

Given data Premise 1: All 9th-floor offices have wall-to-wall carpeting. Premise 2: No wall-to-wall carpeting is pink. Conclusion to test: No 9th-floor office has pink wall-to-wall carpeting. Concept / Approach Use categorical logic: If all items in Group A have Property C, and nothing with Property C can be pink, then nothing in Group A has pink carpeting. Step-by-step reasoning Step 1: Every 9th-floor office ∈ {carpeted}.Step 2: {carpeted} ∩ {pink} = ∅ (by Premise 2, carpets cannot be pink).Step 3: Therefore, for any 9th-floor office, "pink wall-to-wall carpeting" is impossible. Verification / Alternative view Contrapositive thinking: If an office had pink wall-to-wall carpeting, then there would exist pink wall-to-wall carpeting, contradicting Premise 2. Common pitfalls Assuming some 9th-floor offices might lack carpets; Premise 1 rules that out. Final Answer Definitely true.

Question 11

Enrollment comparison puzzle: Class A has a higher enrollment than Class B, and Class C has a lower enrollment than Class B; assess whether the statement "Class A has a lower enrollment than Class C" must be true given only these two premises.

Accepted Answer

Given data Premise 1: A > B (Class A has higher enrollment than Class B). Premise 2: C < B (Class C has lower enrollment than Class B). Claim to test: A < C. Concept / Approach Chain inequalities around B and derive the relative order between A and C. Step-by-step reasoning Step 1: From A > B and C < B, we have A on the right of B and C on the left of B on the number line.Step 2: Therefore A > B > C, which implies A > C.Step 3: The claim A < C contradicts A > C derived above, so it cannot be true under any values consistent with the premises. Verification / Alternative view Example: Let B=30, A=35 (A>B), C=20 (CC. No choice of numbers that respects the premises will make A Common pitfalls Thinking "both are different from B" leaves A and C incomparable. Here, the directions relative to B determine a strict order. Final Answer Definitely false.

Question 12

Logical deduction — apples, lemons, and oranges counts in a basket  Statements: • The basket contains more apples than lemons. • There are more lemons than oranges. Question: If the first two statements are true, is the statement “The basket contain…

Accepted Answer

Introduction / Context: This is a classic transitivity problem in inequality reasoning. When comparing quantities of three categories, we can sometimes chain the comparisons to reach a necessary conclusion about two of them. The challenge is to recognize that “more than” is a transitive relation for strict comparisons. Given Data / Assumptions: Let A = number of apples, L = number of lemons, O = number of oranges. Premise 1: A > L. Premise 2: L > O. All counts are whole numbers (nonnegative integers). Concept / Approach: For strict inequalities on real numbers (and therefore on nonnegative integers), transitivity holds: if x > y and y > z, then x > z. We simply apply this chain to A, L, and O to determine A vs. O. No additional assumptions are required. Step-by-Step Solution: Start with A > L (more apples than lemons).Combine with L > O (more lemons than oranges).By transitivity of “>”, conclude A > O (more apples than oranges).Therefore, the third statement is necessarily true if the first two are true. Verification / Alternative check: Pick sample numbers consistent with the premises: let A = 10, L = 7, O = 3. Both premises hold, and indeed 10 > 3, confirming the derived statement. Any valid triple that satisfies A > L and L > O will automatically satisfy A > O. Why Other Options Are Wrong: false: contradicts the guaranteed inequality chain. uncertain: would apply only if the relation were not transitive or if non-strict comparisons were involved; neither is the case here. both true and false / none of these: distractors that ignore the strict transitivity. Common Pitfalls: Confusing strict “more than” with “at least as many as”, which is non-strict and can break simple transitivity patterns in edge cases. Here, “more than” is strict, so the chain is safe. Final Answer: true

Question 13

Spatial reasoning — relative positions of a store, a pharmacy, and a house  Statements: • The Shop and Save Grocery is south of Greenwood Pharmacy. • Rebecca's house is northeast of Greenwood Pharmacy. Question: If the first two statements are true,…

Accepted Answer

Introduction / Context: This problem examines qualitative spatial reasoning on a grid. Directions like south and northeast constrain relative positions but still leave degrees of freedom. The objective is to decide whether the third statement must hold, given only the first two constraints. Given Data / Assumptions: Let the pharmacy be the origin (0, 0) on an x–y plane. “South of the pharmacy” means the store has y < 0 (x can be any real value). “Northeast of the pharmacy” means the house has x > 0 and y > 0. “West of the store” means the house's x-coordinate is less than the store's x-coordinate. Concept / Approach: We translate each directional statement into coordinate inequalities. If there exist valid placements satisfying the first two statements where the third is true, and also valid placements where the third is false, then the third statement is not determined by the premises and is therefore “uncertain”. Step-by-Step Solution: Place the pharmacy at (0, 0) without loss of generality.Constraint 1: Store S has coordinates (xs, ys) with ys < 0; xs is unconstrained.Constraint 2: House H has coordinates (xh, yh) with xh > 0 and yh > 0.Test a model where the claim is true: Let S = (10, −1), H = (1, 1). Then xh = 1 < xs = 10, so H is west of S. All constraints satisfied.Test a model where the claim is false: Let S = (−10, −1), H = (1, 1). Now xh = 1 > xs = −10, so H is east of S. All constraints still satisfied. Verification / Alternative check: Because both countermodels satisfy the premises but yield opposite truth values for the third statement, the third statement does not necessarily follow; it is indeterminate from the given information. Why Other Options Are Wrong: true or false: each claims a single necessary outcome, but we have consistent scenarios delivering the opposite result. both true and false / none of these: distractors; the correct logical classification is “uncertain”. Common Pitfalls: Assuming “south of” also fixes the x-position (it does not), or assuming “northeast” implies a specific distance or alignment. Only directional quadrants are constrained, leaving room for multiple configurations. Final Answer: uncertain

Question 14

Logical deduction – age order and transitivity Given: Joe is younger than Kathy. Mark was born after Joe (so Mark is younger than Joe). Question: If those two facts are true, is the statement “Kathy is older than Mark” true, false, or uncertain?

Accepted Answer

Introduction / Context: This verbal reasoning item tests your ability to use transitive ordering on ages. If person A is younger than person B, and person C is younger than person A, where does that place C relative to B? You must translate the English statements into a consistent sequence. Given Data / Assumptions: Joe is younger than Kathy. Mark was born after Joe (so Mark is younger than Joe). Claim to evaluate: “Kathy is older than Mark.” Ages are strictly comparable, and “born after” means “younger.” Concept / Approach: Treat “younger than” as a strict order. Use transitivity: if Mark is younger than Joe and Joe is younger than Kathy, then Mark is younger than Kathy. Therefore Kathy is older than Mark. Step-by-Step Solution: 1) Translate: Joe younger than Kathy ⇒ Joe < Kathy.2) Translate: Mark born after Joe ⇒ Mark younger than Joe ⇒ Mark < Joe.3) Chain them: Mark < Joe and Joe < Kathy ⇒ Mark < Kathy.4) Convert back: If Mark is younger than Kathy, then “Kathy is older than Mark” is True. Verification / Alternative check: Pick sample ages: Kathy 15, Joe 13, Mark 12. All statements fit, and the conclusion is clearly true. Why Other Options Are Wrong: False: Contradicts the transitive order. Uncertain: There is no ambiguity; the order is forced by the two premises. Both true and false: Logical truth values are not both simultaneously applicable here. Common Pitfalls: Confusing “born after” (younger) with “older than,” or overlooking transitivity can lead to uncertainty where none exists. Final Answer: True

Question 15

Logical deduction – comparing newborn weights Given: Jenna weighs more than Jason. Jason weighs less than Jasmine. Question: If those two facts are true on the birth day, is the statement “Of the three babies, Jasmine weighs the most” true, false, o…

Accepted Answer

Introduction / Context: This problem evaluates whether you can infer a maximum from pairwise comparisons. Knowing A > B and C > B does not automatically tell you whether A or C is the greatest unless you also know A vs. C. Given Data / Assumptions: Jenna > Jason. Jason < Jasmine (so Jasmine > Jason). Claim to evaluate: “Jasmine is the heaviest of the three.” No direct information about Jenna vs. Jasmine. Concept / Approach: To assert the absolute heaviest, you must compare all contenders. Here we only know both Jenna and Jasmine are heavier than Jason. The order between Jenna and Jasmine is unknown, so the identity of the heaviest is indeterminate. Step-by-Step Solution: 1) From Jenna > Jason and Jasmine > Jason, Jason is the lightest.2) No relation is given between Jenna and Jasmine.3) Therefore, the statement “Jasmine is the heaviest” cannot be guaranteed. Verification / Alternative check: Example 1: Jenna 3.4 kg, Jasmine 3.2 kg, Jason 3.0 kg ⇒ Jasmine is not the heaviest. Example 2: Jenna 3.2 kg, Jasmine 3.4 kg, Jason 3.0 kg ⇒ Jasmine is the heaviest. Since both scenarios fit the premises, the conclusion is uncertain. Why Other Options Are Wrong: True: Not compelled by the premises. False: Also not compelled; there exist cases where it is true. Both true and false: In logic, we label this as “cannot be determined,” not simultaneously true and false. Common Pitfalls: Assuming that because two people are heavier than a third, the second named must be the heaviest overall; this ignores the missing comparison. Final Answer: Uncertain

Question 16

Logical deduction – temperature comparisons across three days Given: Monday was lower than Tuesday. Wednesday was lower than Tuesday. Question: If those two facts are true, is the statement “Monday was higher than Wednesday” true, false, or uncertai…

Accepted Answer

Introduction / Context: This question tests comparative reasoning with inequalities. Knowing two values are both below a third does not tell you their order relative to each other unless additional information is provided. Given Data / Assumptions: Monday < Tuesday. Wednesday < Tuesday. Claim to evaluate: “Monday > Wednesday.” Concept / Approach: From A < C and B < C, nothing follows about A vs. B. Either A > B, A = B, or A < B could be true while still satisfying the premises. Step-by-Step Solution: 1) Represent temperatures numerically: let Tuesday = 30.2) Pick Monday = 25 and Wednesday = 24 ⇒ Monday > Wednesday (conclusion true).3) Pick Monday = 24 and Wednesday = 25 ⇒ Monday < Wednesday (conclusion false).4) Both scenarios satisfy the premises; hence the conclusion cannot be determined. Verification / Alternative check: The uncertainty persists regardless of specific values so long as both days are below Tuesday. Why Other Options Are Wrong: True or False: Each can be made to hold with different consistent assignments, so neither is forced. Both true and false: Not a valid single truth value; the correct label is “Uncertain.” Common Pitfalls: Assuming a default order between Monday and Wednesday because both are lower than Tuesday; that inference is invalid. Final Answer: Uncertain

Question 17

Logical deduction – ordering by fiber content among cereals Given: Oat has more fiber than corn but less than bran. Corn has more fiber than rice but less than wheat. Question: Considering oat, corn, and rice, is the statement “Rice cereal has the l…

Accepted Answer

Introduction / Context: The task is to synthesize two comparative chains to determine the relative order among selected items. Although more cereals are mentioned, the conclusion focuses on three specific kinds: oat, corn, and rice. Given Data / Assumptions: Oat > corn and Oat < bran. Corn > rice and Corn < wheat. Claim to evaluate: “Among oat, corn, and rice, rice has the least fiber.” We only need the order among oat, corn, rice. Concept / Approach: From the second premise, corn is above rice. From the first, oat is above corn. Transitivity then gives oat > corn > rice for the trio of interest, establishing rice as least. Step-by-Step Solution: 1) From “Corn > rice” we know rice is below corn.2) From “Oat > corn” we position oat above corn.3) Combine: Oat > corn > rice.4) Therefore, rice is the least among oat, corn, and rice ⇒ statement is True. Verification / Alternative check: Assign sample numbers: rice 2, corn 3, oat 5, wheat 6, bran 7. All premises hold and rice is indeed least among the specified three. Why Other Options Are Wrong: False / Uncertain: The chain uniquely determines the order; there is no ambiguity. Both true and false: Not applicable; a single consistent order arises. Common Pitfalls: Being distracted by wheat and bran. They help place corn and oat but are not needed to decide the least among oat, corn, and rice. Final Answer: True

Question 18

Logical deduction – seating order behind one another Given: Martina is behind Jerome. Jerome is behind Bryant. Question: If those two facts are true, is the statement “Bryant is behind Martina” true, false, or uncertain?

Accepted Answer

Introduction / Context: This question uses linear order in a classroom-like queue. “Behind” indicates a position farther back from the front. We must determine whether a third claim is consistent with, required by, or contradicted by the initial two. Given Data / Assumptions: Martina is behind Jerome. Jerome is behind Bryant. Claim to evaluate: “Bryant is behind Martina.” All three sit on the same straight line toward the front. Concept / Approach: From the two premises, the order from front to back must be: Bryant, then Jerome, then Martina. If Bryant is ahead of Jerome, and Jerome is ahead of Martina, Bryant cannot be behind Martina. Step-by-Step Solution: 1) Translate: “A behind B” ⇒ B ahead of A.2) From Jerome behind Bryant ⇒ Bryant ahead of Jerome.3) From Martina behind Jerome ⇒ Jerome ahead of Martina.4) Chain: Bryant ahead of Jerome ahead of Martina.5) Conclusion: “Bryant behind Martina” contradicts the forced order ⇒ False. Verification / Alternative check: Visualize three desks in a column; mark them Front → Back as B, J, M. The third statement is incompatible with this arrangement. Why Other Options Are Wrong: True: Directly contradicts the established order. Uncertain: There is no ambiguity; the order is fixed. Both true and false: Not a valid outcome in a consistent linear order. Common Pitfalls: Reversing “behind” and “ahead” or thinking of circular arrangements. The context implies a straight sequence. Final Answer: False

Question 19

Logical deduction – comparing battery life across three products Given: Battery X lasts longer than Battery Y. Battery Y lasts less than Battery Z. Question: If those two facts are true, is the statement “Battery Z lasts longer than Battery X” true,…

Accepted Answer

Introduction / Context: This is a classic inequality-chain problem. We know X > Y and Z > Y. That alone does not establish a direct order between X and Z. You must check if the third claim is logically forced by the premises or not. Given Data / Assumptions: X > Y. Z > Y. Claim to evaluate: “Z > X.” Concept / Approach: From X > Y and Z > Y, X and Z are both above Y. But their relative order remains unknown; Z could be greater than, less than, or equal to X, while still keeping both greater than Y. Step-by-Step Solution: 1) Example A: Let Y = 5, X = 8, Z = 9 ⇒ Z > X (claim True).2) Example B: Let Y = 5, X = 9, Z = 8 ⇒ Z < X (claim False).3) Since both assignments satisfy the premises, the truth of the claim cannot be determined. Verification / Alternative check: The uncertainty is structural: the premises do not compare X and Z directly, so the conclusion is not compelled. Why Other Options Are Wrong: True / False: Each can be made true by a different consistent assignment. Both true and false: A single conclusion cannot have both values; instead we classify the outcome as “Uncertain.” Common Pitfalls: Assuming transitivity from two separate comparisons with a common middle (Y) when the necessary link between X and Z is missing. Final Answer: Uncertain

Question 20

Logical deduction – ordering animal sizes Given: Spot is bigger than King and smaller than Sugar. Ralph is smaller than Sugar and bigger than Spot. Question: If those two facts are true, is the statement “King is bigger than Ralph” true, false, or u…

Accepted Answer

Introduction / Context: We are given two size chains involving four animals. The task is to merge them into a single consistent order and test the truth of the claim about King versus Ralph. Given Data / Assumptions: King < Spot < Sugar. Spot < Ralph < Sugar. Claim to evaluate: “King is bigger than Ralph.” Concept / Approach: Combine the chains by aligning the common elements. From both, Spot is between King and Sugar, and Ralph is above Spot but still below Sugar. Therefore, Ralph is above King. Step-by-Step Solution: 1) From chain 1: K < Spt < Sug.2) From chain 2: Spt < Rlf < Sug.3) Merge: K < Spt < Rlf < Sug.4) Compare King vs. Ralph: K < Rlf ⇒ the statement “King is bigger than Ralph” is False. Verification / Alternative check: Assign sample sizes: King 10, Spot 12, Ralph 13, Sugar 15. All premises hold and the conclusion is clearly false. Why Other Options Are Wrong: True: Opposite of what the merged order shows. Uncertain: The order is fully determined; no ambiguity remains. Both true and false: Not applicable in a strict ordering. Common Pitfalls: Misreading any inequality or forgetting to integrate both chains around the common element Spot. Final Answer: False

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