First slide

Introduction to mathematical reasoning

Question

Statement $(p \lor q) \to (p \land q)$ is equivalent

Easy

A

$F$
B

$p \leftrightarrow q$
C

$T$
D

$q \to p \land q$

Solution

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

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