Let $p, q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$…

Question

Let $p, q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is

Accepted Answer

Correct answer: D — Key observations: If (p→q)→r is a contradiction, then for every valuation the antecedent (p→q) must be true and r must be false. So p→q is a tautology and r is a contradiction (r is always false). Because r is always false, r→p is always true (false implies anything). Therefore (r→p)→q simplifies to true→q, which is logically equivalent to q. Conclusion: The expression (r→p)→q is equivalent to q, so it is always true whenever q is true.

Answer

A. a tautology

Answer

B. a contradiction

Answer

C. always TRUE when $p$ is FALSE

Answer

D. always TRUE when $q$ is TRUE

Let \(p, q\) and \(r\) be propositions and the expression \(\left (…