Question

Statements: Some fishes are cats.
Some dogs are cats.
No fish is black.
Conclusions: I. At least some cats are not black.
II. There is a possibility that some fishes are dogs.

• 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 $Fishes=F$, $Cats=C$, $Dogs=D$ and $Black=B$.

Staements:

$1)F\cap C\ne \Phi$

$2)D\cap C\ne \Phi$

$3)F\cap B=\Phi$

Conclusion-I : $C\cap B^{\prime }\ne \Phi$

which doesn't contradict any of the statements.

So, conclusion-I follows.

Conclusion-II : $F\cap D\ne \Phi$

which doesn't contradict any of the statements.

So, conclusion-II follows.

$\therefore$ The answer is $\left[E\right]$.