The question contains some statements followed by some conclusions. Decide…
2023
The question contains some statements followed by some conclusions. Decide which of the given conclusions logically follow from the given statements, disregarding commonly known facts.
Statements
P: Some children are adults.
Q: Some adults are not old
Conclusions
I. Some children are not old.
II. Some children are old.
- A.
Only I follows
- B.
Only II follows
- C.
Neither I nor II follows
- D.
Both I and II follows
Attempted by 74 students.
Show answer & explanation
Correct answer: C
Given statements: Some children are adults. Some adults are not old.
Key idea: The two statements allow multiple arrangements of how the sets overlap, so a conclusion requires a guarantee in all possible arrangements.
Why the conclusion "Some children are not old" does not follow: The overlap between children and adults could lie entirely within the adults who are old, while the adults who are not old are separate. In that arrangement the first statement (some children are adults) and the second statement (some adults are not old) are both true, but there are no children who are not old.
Why the conclusion "Some children are old" does not follow: It is also possible that the overlap between children and adults lies entirely within the adults who are not old. Then both given statements hold but no child is old.
Conclusion: Neither conclusion is guaranteed by the statements, so the correct answer is the choice that says "Neither I nor II follows."