Question 1

Syllogism (logical deduction): Evaluate the conclusions based on the given statements.  Statements: S1: Some actors are singers. S2: All the singers are dancers.  Conclusions: C1: Some actors are dancers. C2: No singer is actor.  Choose the option t…

Accepted Answer

Given data S1: Some actors are singers. S2: All singers are dancers. Conclusions to test: C1 (Some actors are dancers), C2 (No singer is actor). Concept / Approach Use set relations: If some Actors ∩ Singers ≠ ∅ and Singers ⊆ Dancers, then those same actors are also Dancers. A universal negative about singers vs actors contradicts S1. Step-by-step check From S1: ∃x such that x ∈ Actors and x ∈ Singers. From S2: Singers ⊆ Dancers ⇒ Any singer is a dancer. Therefore that x is also a Dancer ⇒ Some actors are dancers ⇒ C1 is true. C2 says “No singer is actor,” which directly contradicts S1 ⇒ C2 is false. Common pitfalls Assuming “some” means “all,” or overlooking subset propagation (Singers ⊆ Dancers). Final Answer Only conclusion I follows.

Question 2

Syllogism (set inclusion): Decide which conclusion(s) logically follow from the statements.  Statements: S1: All the harmoniums are instruments. S2: All the instruments are flutes.  Conclusions: C1: All the flutes are instruments. C2: All the harmon…

Accepted Answer

Given data S1: Harmoniums ⊆ Instruments. S2: Instruments ⊆ Flutes. Conclusions: C1 “All flutes are instruments,” C2 “All harmoniums are flutes.” Concept / Approach Subset chaining: If A ⊆ B and B ⊆ C, then A ⊆ C. Converse statements are not guaranteed. Testing conclusions From S1 and S2: Harmoniums ⊆ Instruments ⊆ Flutes ⇒ Harmoniums ⊆ Flutes ⇒ C2 is true. C1 is the converse of S2 (claims Flutes ⊆ Instruments). S2 only gives Instruments ⊆ Flutes, not the reverse ⇒ C1 is not guaranteed. Final Answer Only conclusion II follows.

Question 3

Syllogism (categorical reasoning): Determine which conclusions follow strictly.  Statements: S1: Some mangoes are yellow. S2: Some tixo are mangoes.  Conclusions: C1: Some mangoes are green. C2: Tixo is a yellow.  Choose the correct option according…

Accepted Answer

Given data S1: Some Mangoes are Yellow (existential statement about Yellow mangoes). S2: Some Tixo are Mangoes (existential statement linking Tixo to Mangoes). Concept / Approach “Some” statements do not force overlap with other “Some” statements unless explicitly connected. No information is given about “green,” and there is no necessary overlap between the specific yellow mangoes of S1 and the specific mangoes related to Tixo in S2. Testing conclusions C1: “Some mangoes are green” is unsupported; color “green” is never mentioned. C2: From S1 and S2, we cannot conclude Tixo are Yellow, because the “some mangoes” related to Tixo need not be the same “some mangoes” that are Yellow. Final Answer Neither I nor II follows.

Question 4

Syllogism (set chaining): Identify which conclusions follow from the premises.  Statements: S1: Some ants are parrots. S2: All the parrots are apples.  Conclusions: C1: All the apples are parrots. C2: Some ants are apples.  Choose the correct option.

Accepted Answer

Given data S1: ∃x such that x ∈ Ants and x ∈ Parrots. S2: Parrots ⊆ Apples. Concept / Approach When some Ants are Parrots and every Parrot is an Apple, those same Ants are Apples. The converse universal claim about Apples need not hold. Testing conclusions C2: True, because the intersecting elements from S1 are inside Parrots, and all Parrots are Apples ⇒ Some Ants are Apples. C1: False, because S2 gives Parrots ⊆ Apples, not Apples ⊆ Parrots. Final Answer Only conclusion II follows.

Question 5

Syllogism (pens, pencils, papers): Determine which conclusions must be true.  Statements: S1: Some papers are pens. S2: All the pencils are pens.  Conclusions: C1: Some pens are pencils. C2: Some pens are papers.  Choose the correct option.

Accepted Answer

Given data S1: Some Papers ∩ Pens ≠ ∅. S2: Pencils ⊆ Pens. Concept / Approach Universal inclusion does not imply existence. From S2 alone, we cannot assert that any Pencil exists to guarantee “Some pens are pencils.” But S1 already guarantees at least one Pen that is also a Paper. Testing conclusions C1: Not guaranteed; there may be no Pencils at all. “All Pencils are Pens” does not ensure “Some Pens are Pencils.” C2: Guaranteed by S1, because if some Papers are Pens, then some Pens are Papers (same intersection). Final Answer Only conclusion II follows.

Question 6

Syllogism (actors, girls, beautiful): Evaluate the validity of the conclusions.  Statements: S1: All the actors are girls. S2: All the girls are beautiful.  Conclusions: C1: All the actors are beautiful. C2: Some girls are actors.  Choose the correc…

Accepted Answer

Given data S1: Actors ⊆ Girls. S2: Girls ⊆ Beautiful. Concept / Approach Subset chaining: If Actors ⊆ Girls and Girls ⊆ Beautiful, then Actors ⊆ Beautiful. The statement “Some Girls are Actors” requires existential import for Actors, which is not guaranteed by universal statements alone. Testing conclusions C1: True by transitivity ⇒ Actors ⊆ Beautiful. C2: Not guaranteed; from universals alone, we cannot assert existence of Actors. Final Answer Only conclusion I follows.

Question 7

Syllogism (windows, doors, walls): Decide which conclusion(s) follow logically.  Statements: S1: All the windows are doors. S2: No door is a wall.  Conclusions: C1: Some windows are walls. C2: No wall is a door.  Choose the correct option.

Accepted Answer

Given data S1: Windows ⊆ Doors. S2: Doors ∩ Walls = ∅ (No door is a wall). Concept / Approach From S2, the disjointness is symmetric: If no A is B, then no B is A. Also, since Windows are a subset of Doors, Windows cannot overlap with Walls. Testing conclusions C1: “Some windows are walls” contradicts S1+S2, because any Window is a Door and no Door is a Wall. C2: “No wall is a door” is the contrapositive-symmetric form of S2, valid for disjointness statements. Final Answer Only conclusion II follows.

Question 8

Syllogism: Evaluate which conclusions logically follow from the given statements (Venn-diagram reasoning).  Statements: All cups are books. All books are shirts.  Conclusions: I. Some cups are not shirts. II. Some shirts are cups.  Choose the correc…

Accepted Answer

Given data Statement 1: All cups ⊆ books. Statement 2: All books ⊆ shirts. Therefore: All cups ⊆ shirts. Conclusions to test: (I) Some cups are not shirts; (II) Some shirts are cups. Concept/Approach Translate universal statements into set containment and test each conclusion against all possible Venn diagrams consistent with the premises. From All cups ⊆ books and All books ⊆ shirts, it follows that all cups are inside shirts. Step-by-step evaluation Conclusion I: "Some cups are not shirts" contradicts All cups ⊆ shirts, so it does not follow. Conclusion II: Since cups are a subset of shirts and we assume the existence of at least one cup (standard syllogism convention in such MCQs), at least one element is both a shirt and a cup; hence "Some shirts are cups" follows. Common pitfalls Confusing the converse ("Some shirts are cups") with the original universal; here, particular existence is acceptable under exam conventions. Final Answer Only Conclusion II follows

Question 9

Syllogism: Evaluate which conclusions logically follow from the given statements (possibility vs. necessity).  Statements: Some cows are crows. Some crows are elephants.  Conclusions: I. Some cows are elephants. II. All crows are elephants.  Choose …

Accepted Answer

Given data Some cows ∩ crows ≠ ∅. Some crows ∩ elephants ≠ ∅. Conclusions to test: (I) Some cows ∩ elephants ≠ ∅; (II) All crows ⊆ elephants. Concept/Approach "Some–Some" premises do not force an overlap between the first and third sets; the overlapping parts of crows could be disjoint (different crows in each statement). Step-by-step evaluation Conclusion I: It is only a possibility, not a necessity. There exist valid diagrams where cows and elephants do not overlap, so it does not follow. Conclusion II: "All crows are elephants" is far stronger than the premises and does not follow. Final Answer Neither Conclusion I nor II follows

Question 10

Syllogism: Determine which conclusions must follow from the chain of containments.  Statements: All the pencils are pens. All the pens are inks.  Conclusions: I. All the pencils are inks. II. Some inks are pencils.  Choose the correct option about w…

Accepted Answer

Given data All pencils ⊆ pens; All pens ⊆ inks ⇒ All pencils ⊆ inks. Conclusions: (I) All pencils are inks; (II) Some inks are pencils. Concept/Approach Transitivity of containment validates I. Under standard MCQ convention assuming existence of pencils, at least one pencil exists, so that element is an ink; hence "Some inks are pencils" holds. Step-by-step evaluation I: Directly true by transitivity (pencils ⊆ inks). II: From existence of at least one pencil in the subset, "some" particular of inks is indeed a pencil. Final Answer Both Conclusions I and II follow

Question 11

Syllogism: Assess whether the given pairwise "some" statements force an overlap between outer sets.  Statements: Some dogs are bats. Some bats are cats.  Conclusions: I. Some dogs are cats. II. Some cats are dogs.  Choose the correct option about wh…

Accepted Answer

Given data Some dogs overlap with bats; some bats overlap with cats. Middle term is "bats". Concept/Approach Two separate "some" overlaps via a middle set do not compel dogs and cats to overlap; the overlapping bats could be different individuals. Evaluation Both I and II are mere possibilities, not necessary conclusions. Hence neither follows. Final Answer Neither Conclusion I nor II follows

Question 12

Syllogism: Decide which conclusions necessarily follow from the category statements.  Statements: All the trucks are flies. Some scooters are flies.  Conclusions: I. All the trucks are scooters. II. Some scooters are trucks.  Choose the correct opti…

Accepted Answer

Given data All trucks ⊆ flies; Some scooters ∩ flies ≠ ∅. No direct relation between "trucks" and "scooters" is compelled. Analysis I: "All trucks are scooters" is not forced—trucks could be a different subset of flies. II: "Some scooters are trucks" is also not necessary—overlap may or may not exist. Final Answer Neither Conclusion I nor II follows

Question 13

Syllogism: Test the conclusions using set relations and complement information.  Statements: All buildings are chalks. No chalk is toffee.  Conclusions: I. No building is toffee. II. All chalks are buildings.  Choose the correct option about which c…

Accepted Answer

Given data All buildings ⊆ chalks. No chalk ∩ toffee ≠ ∅ (i.e., chalks and toffee are disjoint). Reasoning If every building is a chalk and chalks have no overlap with toffee, then buildings cannot be toffee. Thus I follows. "All chalks are buildings" is the converse of the first statement and does not follow. Final Answer Only Conclusion I follows

Question 14

Syllogism: Determine the logically valid conclusion(s) based on two subset statements with a common superser.  Statements: All cars are cats. All fans are cats.  Conclusions: I. All cars are fans. II. Some fans are cars.  Choose the correct option a…

Accepted Answer

Given data Cars ⊆ cats; Fans ⊆ cats. No direct relationship stated between cars and fans. Evaluation I: "All cars are fans" need not be true; both could be disjoint subsets of cats. II: "Some fans are cars" is only a possibility, not a necessity. Final Answer Neither Conclusion I nor II follows

Question 15

Statements: No door is dog. All the dogs are cats. Conclusions: No door is cat. No cat is door. Some cats are dogs. All the cats are dogs.

Accepted Answer

Question 16

Statements: All green are blue. All blue are white. Conclusions: Some blue are green. Some white are green. Some green are not white. All white are blue.

Accepted Answer

Question 17

Statements: All men are vertebrates. Some mammals are vertebrates. Conclusions: All men are mammals. All mammals are men. Some vertebrates are mammals. All vertebrates are men.

Accepted Answer

Question 18

Statements: All the phones are scales. All the scales are calculators. Conclusions: All the calculators are scales. All the phones are calculators All the scales are phones. Some calculators are phones.

Accepted Answer

Question 19

Statements: Some tables are T.V. Some T.V. are radios. Conclusions: Some tables are radios. Some radios are tables. All the radios are T.V. All the T.V. are tables.

Accepted Answer

Question 20

Statements: Some pens are books. Some books are pencils. Conclusions: Some pens are pencils. Some pencils are pens. All pencils are pens. All books are pens.

Accepted Answer

Syllogism Questions