First slide

Introduction to mathematical reasoning

Question

Which of the following is equivalent to $p \leftrightarrow q ?$

Easy

A

$(~ p \lor q) \lor (p \lor q)$
B

$(p \land q) \lor (~ p \land ~ q)$
C

$(p \lor q) \land (p \lor ~ q)$
D

$(p \land q) \lor (p \lor q)$

Solution

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

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