Question

The negation of $A\to (A\vee \sim B)$

• A. a fallacy
• B. equivalent to $(A\wedge \sim B)\to A$
• C. equivalent to $(A\vee \sim B)\to A$
• D. a tautology

Answer 1

The correct option is A

a fallacy

Consider the table below:

$\begin{array}{cccccc}A& B& \sim B& A\vee \sim B& A\to (A\vee \sim B)& \sim (A\to (A\vee \sim B)\\ T& F& T& T& T& F\\ F& T& F& F& T& F\end{array}$

So, the negation of $A\to (A\vee \sim B)$ is fallacy