Question

In each question below are given two or three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answer
Statements: Some balls are locks.
All locks are keys.
Some doors are keys.
Conclusions: I. At least some balls are doors.
II. All doors being locks is a possibility.

• A. if only conclusion I follows.
• B. if only conclusion II follows.
• C. if either conclusion I or II follows.
• D. if neither conclusion I nor II follows.
• E. if both conclusions I and II follow.

Answer 1

Answer: (E)

if both conclusions I and II follow.

Let $Balls=B$, $Locks=L$, $Doors=D$ and $Keys=K$.

Statements:

$1)B\cap L\ne \Phi$

$2)L\subset K$

$3)D\cap K\ne \Phi$

Conclusion-I : $B\cap D\ne \Phi$

which doesn't contradict any statements.

So, conclusion-I follows.

Conclusion-II : $D\subset L$

This can be true. Doesn't contradict any of the statements.

So, conclusion-II follows.

The answer is $\left[E\right]$. Both conclusions follow.