First slide

Introduction to mathematical reasoning

Question

Which one of the following is a tautology?

Moderate

A

$P \lor (P \land Q)$
B

$Q \to (P \land (P \to Q))$
C

$P \land (P \lor Q)$
D

$(P \land (P \to Q)) \to Q$

Solution

$\begin{array}{cccccccccl} p & q & p \to q & p \land (p \to q) & (p \land (p \to q)) \to q & q \to p \land (p \to q) & p \land q & p \lor (p \land q) & p \lor q & p \land (p \lor q) \\ T & T & T & T & T & T & T & T & T & T \\ T & F & F & F & T & T & F & T & T & T \\ F & T & T & F & T & F & F & F & T & F \\ F & F & T & F & T & T & F & F & F & F \end{array}$

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