Which of the following are correct (valid) ways of reasoning?

1.There can be no second husband without there having been a second marriage

2.Anil is a friend of Bob; Bob is a friend of Raj; hence Anil is a friend of Raj

3.A is equal to B; B is equal to C; hence A is equal to C

4.If everyone is a liar, then we cannot prove it

A3 and 4 ✓ Correct

B1 and 3

C2, 3 and 4

D1, 2, 3 and 4

Correct answer: (A) 3 and 4

Explanation

Valid reasoning appears in the equality chain and the liar conditional, Statements 3 and 4.

Statement 3 applies the transitivity of equality, so A equal to B and B equal to C yields A equal to C.

This chaining is licensed because equality is a genuinely transitive relation.

Statement 4 reasons soundly that if everyone always lies, any asserted proof is itself false.

With every statement false no proof can stand, so the claim indeed cannot be proved.

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