First slide

Introduction to mathematical reasoning

Question

The negation of $A \to (A \lor ~ B)$ is

Easy

A

a tautologa
B

equivalent to $(A \lor ~ B) \to A$
C

equivalent to $A \to (A \land ~ B)$
D

a fallacy

Solution

$\begin{aligned} A \to (A \lor ~ B) \\ \equiv ~ A \lor (A \lor ~ B) \\ \equiv (~ A \lor A) \lor (~ B) \\ \equiv T \lor (~ B) \equiv T \end{aligned}$
$∴$ Negative of $A \to A \lor ~ B is ~ T = F .$

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