First slide

Introduction to mathematical reasoning

Question

$The inverse of the proposition (p \land ~ q) \to r is$

Moderate

A

$r \Rightarrow p \land ~ q$
B

$~ p \Rightarrow p \lor q$
C

$~ p \lor q \Rightarrow ~ r$
D

None of these

Solution

$Inverse of p \Rightarrow q is ~ p \Rightarrow\sim q$
$Inverse of (p \land ~ q) \Rightarrow r is ~ (p^{\land} ~ q) \Rightarrow\sim r . Thus,$ $(~ p \lor q) \Rightarrow\sim r$
Hence, (c) is true.

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