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 $p v q$
D

is a contradiction

Solution

$\begin{array}{l} ~ (p \land q) \lor q \\ \equiv ((~ p) \lor (~ q)) \lor q \\ \equiv (~ p) \lor ((~ q) \lor q) \\ = (~ p) \lor t = t \end{array}$
Thus $~ (p \land q) \lor q$ is a tautology.

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