Question

Statement: No cats are dogs.
Conclusion: No dogs are cats.
Is the conclusion valid?

• A. Yes
• B. No
• C. Partially valid
• D. Cannot determine

Hint:

For "no" statements, check for symmetry in logical conclusions.

Answer 1

The Correct Option is A

- Step 1: Analyze the statement. "No cats are dogs" means the sets of cats and dogs are disjoint (C \cap D = \emptyset).
- Step 2: Evaluate the conclusion. "No dogs are cats" means D \cap C = \emptyset, which is the same as C \cap D = \emptyset.
- Step 3: Apply logical reasoning. The statement is symmetric; if no cats are dogs, no dogs are cats.
- Step 4: Test for validity. The conclusion restates the disjoint nature of the sets, so it is valid.
- Step 5: Check options. Option (1) "Yes" is correct. Option (2) "No" is incorrect. Option (3) "Partially valid" is not applicable. Option (4) "Cannot determine" is incorrect as the conclusion follows.
- Step 6: Conclusion. Option (1) is correct.