Two statements are given, followed by two conclusions numbered 1 and 2. Assuming the statements to be true, even if they seem to be at variance with known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All hooks are hangers.
Some hangers are locks.
Conclusions:
Some locks are hangers
All locks are hooks.
- AOnly conclusion 1 follows
- BNeither conclusion 1 nor 2 follows
- COnly conclusion 2 follows
- DBoth conclusions 1 and 2 follow
Solution & Step-by-step Explanation
Let's analyze the statements:
Statement 1: All hooks are hangers.
Statement 2: Some hangers are locks.
Evaluating the conclusions:
Some locks are hangers: Since 'Some hangers are locks', the intersection between locks and hangers is non-empty. Therefore, some locks are definitely hangers. This conclusion follows.
All locks are hooks: There is no definitive connection established between locks and hooks from the premises. Hence, this conclusion does not follow.
Therefore, only conclusion 1 follows.
Statement 1: All hooks are hangers.
Statement 2: Some hangers are locks.
Evaluating the conclusions:
Some locks are hangers: Since 'Some hangers are locks', the intersection between locks and hangers is non-empty. Therefore, some locks are definitely hangers. This conclusion follows.
All locks are hooks: There is no definitive connection established between locks and hooks from the premises. Hence, this conclusion does not follow.
Therefore, only conclusion 1 follows.