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The statement among the following that is a tautology is:

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

$A \land (A \lor B)$

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

$A \lor (A \land B)$

answer is A.

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Detailed 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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