First slide

Introduction to mathematical reasoning

Question

Let p, q and r be three statements, then $(p \to q) \to r$ is equivalent to

Easy

A

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

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

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

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

Solution

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

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