Logical reasoning – syllogism with two premises: ‘‘Some papers are pens’’ and ‘‘Some pencils are pens’’ – determine which conclusions logically follow about overlaps among pens, pencils, and papers.
Verbal Reasoning
Logical Deduction
Difficulty: Medium
Choose an option
-
AOnly conclusion I follows
-
BOnly conclusion II follows
-
CEither I or II follows
-
DNeither I nor II follows
-
EBoth I and II follow
Answer
Correct Answer: Both I and II follow
Explanation
Premises: Some papers are pens. Some pencils are pens. Conclusions to test: (I) Some pens are pencils. (II) Some pens are papers.
Concept/ApproachTranslate each statement into set language and use basic syllogistic/venn reasoning. ‘‘Some X are Y’’ guarantees a non-empty overlap between X and Y. The converse phrasing ‘‘Some Y are X’’ is also true for particular statements.Step-by-step evaluation• From ‘‘Some pencils are pens’’ ⇒ There exists at least one object that is both a pencil and a pen ⇒ ‘‘Some pens are pencils’’ (Conclusion I) is true.• From ‘‘Some papers are pens’’ ⇒ There exists at least one object that is both a paper and a pen ⇒ ‘‘Some pens are papers’’ (Conclusion II) is true.Verification/AlternativeDraw three overlapping circles (Pens, Pencils, Papers). Shade one element in Pens∩Pencils and one element in Pens∩Papers. Both conclusions are immediately visible.Common pitfalls• Assuming ‘‘Some X are Y’’ implies ‘‘All X are Y.’’ It does not; we only need at least one common element.Final AnswerBoth I and II follow.