Question

The statement among the following that is a tautology is:

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

Answer 1

The correct option is D

$\left[A\to (A\to B)\right]\to B$

Explanation for the correct option:

Option (D): $\left[A\to (A\to B)\right]\to B$

So,

$$\begin{gathered} A\wedge (~A\vee B)\to B \\ =\left[\right(A\wedge ~A)\vee (A\wedge B\left)\right]\to B \\ =(A\wedge B)\to B \\ =~(A\wedge B)\vee B \\ =t \end{gathered}$$

Hence, option (D), $\left[A\to (A\to B)\right]\to B$ is the correct answer.