Question

The statement among the following that is a tautology is:

• A. $A\wedge (A\vee B)$
• B. $B\to [A\wedge (A\to B\left)\right]$
• C. $A\vee (A\wedge B)$
• D. $[A\vee (A\to B\left)\right]\to B$

Answer 1

The correct option is D $[A\vee (A\to B\left)\right]\to B$

$A\wedge (\sim A\vee B)\to B$
$=\left[\right(A\wedge \sim A)\vee (A\wedge B\left)\right]\to B$
$=(A\wedge B)\to B$
$=\sim (A\wedge B)\vee B$
$=t$