First slide

Introduction to mathematical reasoning

Question

The statement among the following that is a tautology is:

Moderate

A

$[A \land (A \to B)] \to B$
B

$A \land (A \lor B)$
C

$B \to [A \land (A \to B)]$
D

$A \lor (A \land B)$

Solution

$\begin{matrix} [A \land (~ A \lor B)] \to B = [(A \land ~ A) \lor (A \land B)] \to B \\ = (A \land B) \to B \end{matrix}$
A B A $\land$ B A $\land$ B $\Rightarrow$ B
T T T T
T F F T
F T F T
F F F T
$∴ [A \land (~ A \lor B)] \to B i s a t a u t o \log y$

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