First slide

Introduction to mathematical reasoning

Question

$Which of the following is true?$

Moderate

A

$~ p \land (p \Leftrightarrow q) \equiv [~ (p \Rightarrow q) \land ~ (q \Rightarrow p)]$
B

$p \Rightarrow q \equiv\sim p \Rightarrow\sim q$
C

$~ (p \Rightarrow\sim q) \equiv\sim p \land q$
D

$~ (~ p \Rightarrow\sim q) \equiv\sim p \land q$

Solution

$\begin{array}{l} ~ (p \Rightarrow q) \equiv ~ (p \land ~ q) \\ ~ (~ p \Rightarrow\sim q) \equiv\sim p \land ~ (~ q) \equiv ~ p \land q \\ Thus ~ (~ p \Rightarrow\sim q) \equiv ~ p \land q \end{array}$
Hence, (d) is the correct answer.

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