First slide

Introduction to mathematical reasoning

Question

The statement $~ (p \land q) \lor q :$

Easy

A

is a tautology
B

is equivalent to $(p \land q) \lor ~ q$
C

is equivalent to $p \lor q$
D

is a contradiction

Solution

$\begin{aligned} ~ (p \land q) \lor q \\ \equiv (~ p \lor ~ q) \lor q \\ \equiv\sim p \lor (~ q \lor q) \\ \equiv\sim p \lor T \equiv T \end{aligned}$

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