First slide

Introduction to mathematical reasoning

Question

$(p \land ~ q) \land (~ p \land q)$ is

Moderate

A

a tautology
B

a contradiction
C

neither a tautology nor a contradiction
D

None of these

Solution

$\begin{array}{l} (p \land ~ q) \land (~ p \land q) \\ \equiv (p \land ~ p) \land (~ q \land q) \\ \equiv f \land f \\ \equiv f (By using associative laws and commutative laws) \end{array}$
Therefore, $(p \land ~ q) \land (~ p \land q)$ is a contradiction.

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