Question

In each question below are given three statements followed by two conclusions numbered I and II. You have to take the given two 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 statements, disregarding commonly known facts. Give answer
Statements: Some bananas are soaps.
Some powders are soaps.
Only detergents are powders.
Conclusions: I. Some soaps are detergents.
II. Some detergents are not soaps

• 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

The correct option is E if both conclusions I and II follow.

Let the set of bananas be $B$, powders be $P$ and soaps be $S$.

($\Phi$ is the null set)

Statements:

$a)B\cap S\ne \Phi$

$b)P\cap S\ne \Phi$

$c)P=powders=detergents$

$Conclusion-I$ : $S\cap detergents\ne \Phi$

$\Rightarrow S\cap P\ne \Phi$ which is given in statement $\left(b\right)$.

$\Rightarrow$ Conclusion-I follows.

$Conclusion-II$ : $S^{\prime }\cap detergents\ne \Phi$

$\Rightarrow S^{\prime }\cap P\ne \Phi$

$\Rightarrow P-P\cap S\ne \Phi$

$\Rightarrow P\ne P\cap S$ (which is possible if P is not a subset of S)

It is not given that P is a subset of S.

$\Rightarrow$ Conclusion-II follows.

So, the answer is $\left[E\right]$.

Both conlusions follow.