First slide

Introduction to mathematical reasoning

Question

Which of the following statement is a contradiction?

Moderate

A

$(~ p \lor ~ q) \lor (p \lor ~ q)$
B

$(p \to q) \lor (p \land ~ q)$
C

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

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

Solution

We consider following truth table
Clearly, last column of the above truth table contains only F. Hence, $(p \land q) \land ~ (p \lor q)$ is a contradiction

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