First slide

Introduction to mathematical reasoning

Question

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

Moderate

A

a contradiction
B

either (1) or (2)
C

a tautology
D

neither (1) nor (2)

Solution

p q $~ p$ $~ q$ $p \land ~ q$ $~ p \lor q$ $(p \land ~ q) \land (~ p \lor q)$
T T F F F T F
T F F T T F F
F T T F F T F
F F T T F T F
Clearly, $(p \land ~ q) \land (~ p \lor q)$ is a contradiction.

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