First slide

Introduction to mathematical reasoning

Question

Which of the following is true?

Easy

A

$p \Rightarrow q \equiv\sim p \Rightarrow\sim q$
B

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

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

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

Solution

$\begin{array}{l} ~ (p \Rightarrow q) \equiv p \land ~ q \\ ∴ ~ (~ p \Rightarrow\sim q) \equiv\sim p \land ~ (~ q) \equiv\sim p \land q \\ Thus, ~ (~ p \Rightarrow\sim q) \equiv\sim p \land q \end{array}$

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