Question

Some dogs are rats. All cats are chairs. All rats are cats.
What can be concluded from the above given statements?
(A) All dogs are cats
(B) All cats are rats
(C) All chairs are dogs
(D) All rats are chairs
Choose the correct answer from the options given below:

• A. Only (A) and (B) follow.
• B. Only (B) follows.
• C. Only (A) and (D) follow.
• D. Only (D) follows.

Hint:

Chain the two universal (All...are) statements first; that always gives a valid conclusion.

Answer 1

The Correct Option is D

Draw the chain of sets step by step.
Rats $\subseteq$ Cats (all rats are cats), and Cats $\subseteq$ Chairs (all cats are chairs). Combining these two universal statements gives Rats $\subseteq$ Chairs, meaning every rat is a chair. So conclusion (D) is certain.
Now check the others by testing possibility, not certainty. Dogs and Rats only overlap partially (some dogs are rats), so we cannot place all dogs inside Cats, only some. So (A) is not forced.
Cats $\subseteq$ Chairs does not mean Chairs $\subseteq$ Cats, so (C) is false, and it also does not mean Cats $\subseteq$ Rats, so (B) is false.
Only one conclusion survives the test of certainty.
\[\boxed{\text{Only (D) follows}}\]