First slide

Introduction to mathematical reasoning

Question

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

Easy

A

$p \land (~ q) \to r$
B

$p \lor (~ r) \to q$
C

$p \land (~ r) \to\sim q$
D

$p \lor (~ r) \to q$ .

Solution

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

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