Question

The statement $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a:

• A. Tautology
• B. Fallacy
• C. Neither tautology nor fallacy
• D. Tautology and fallacy

Answer 1

The correct option is B Fallacy

$p\Rightarrow q$ is false only if p is true and q is false. $p\wedge q$ is true only if p and q are true. The truth table for $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is given below.
$\begin{array}{ccccc}p& \sim p& p\Rightarrow \sim p& \sim p\Rightarrow p& (p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)\\ T& F& F& T& F\\ F& T& T& F& F\end{array}$
The staement is always false. Hence, it is a fallacy.