Question

The conditional $(p\wedge q)\Rightarrow p$ is ___.

• A. A tautology
• B. A fallacy
• C. Neither a tautology nor a fallacy
• D. A contrapositive

Answer 1

The correct option is A A tautology

$p\Rightarrow q$ is false only when p is true and q is false. The truth table for $(p\wedge q)\Rightarrow p$ is shown below.
$\begin{array}{cccc}p& q& p\wedge q& (p\wedge q)\Rightarrow p\\ T& T& T& T\\ T& F& F& T\\ F& T& F& T\\ F& F& F& T\end{array}$
Alternatively, $p\wedge q$ is true only if p is true i.e. whenever p is false, $p\wedge q$ is also false. Hence, $(p\wedge q)\Rightarrow p$ is always true. It is a tautology.