In each of the following questions two statements are given and these…
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In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts.
Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
Statements:
All the pencils are pens.
All the pens are inks.
Conclusions:
All the pencils are inks.
Some inks are pencils.
- A.
Both conclusion follows
- B.
Only (2) conclusion follows
- C.
Either (1) or (2) follows
- D.
Neither (1) nor (2) follows
Attempted by 129 students.
Show answer & explanation
Correct answer: A
Explanation: use the transitive relation of the class inclusion given by the statements.
From "All the pencils are pens" and "All the pens are inks," we conclude that every pencil is also an ink (pencils ⊂ pens ⊂ inks).
Because pencils are a subset of inks and the class of pencils is assumed to be non-empty, there exist inks that are pencils, so "Some inks are pencils" is true.
Conclusion: Both given conclusions follow from the premises: all pencils are inks, and some inks are pencils.
Note: The original solution image indicates that both conclusions follow. The written explanation above makes the reasoning explicit and clarifies that the correct logical outcome is that both conclusions follow.