Two statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All keys are locks.
No door is a lock.
Conclusions:
I. Some locks are doors.
II. Some locks are keys.
III. No key is a door.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. Both conclusions II and III follow.
The least possible Venn Diagram for the given statements is drawn below:
Conclusions:
I. Some locks are doors → False (As no door is a lock, so, some locks can never be doors.)
II. Some locks are keys → True (As all keys are locks, so, some locks are keys is also true.)
III. No key is a door → True (As all keys are locks and no door is a lock, so, no key is a door is also true.)