Consider the following statements r : If p q is false then p q is false. s : If p q is false then p q is false. The truth values of r s and s r are respectively ____

Step-by-step solution

Let us evaluate the truth value of statement r . The premise is " p q is false". The implication p q is false only when p is True (T) and q is False (F). For p = T and q = F , the value of p q is T F = T (True). However, statement r claims that p q is false. Since the conclusion is false when the premise is true, statement r is False (F). Now, let us evaluate the truth value of statement s . The premise is " p q is false". The biconditional p q is false when p and q have opposite truth values. This gives two cases: