First slide

Introduction to mathematical reasoning

Question

: Let p and q be two statements, then $~ (~ p \land q) \land (p \lor q)$ is logically equivalent to

Easy

A

q
B

$p \land q$
C

p
D

$p \lor ~ q$

Solution

$~ (~ p \land q) \land (p \lor q) \equiv [~ (~ p) \lor (~ q)] \land (p \lor q)$
$\begin{array}{l} \equiv [p \lor (~ q) \land (p \lor q] \\ \equiv p \lor [(~ q) \land q] \\ \equiv p \lor F \equiv p \end{array}$

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