First slide

Introduction to mathematical reasoning

Question

$Which of the following is false?$

Moderate

A

$(p \Rightarrow q) \Leftrightarrow (~ q \Rightarrow\sim p) is a contradiction$
B

$p \lor (~ p) is a tautology$
C

$~ (~ p) \Leftrightarrow p is a tautology$
D

$p \land (~ p) is a contradiction$

Solution

$p \Rightarrow q is logically equivalent to ~ q \Rightarrow\sim p, therefore,$
$(p \Rightarrow q) \Leftrightarrow (~ q \Rightarrow\sim p) is a tautology but not a contradiction$
So (a) is false.

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