Question

The only statement among the following that is a tautology is

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

Answer 1

The correct option is D $[a\wedge (a\to b\left)\right]\to b$

$\begin{array}{cccccccccc}a& b& a\vee b& a\wedge b& a\wedge (a\vee b)& a\vee (a\wedge b)& a\to b& a\wedge (a\to b)& a\wedge (a\to b)\to b& b\to a\wedge (a\to b))\\ T& T& T& T& T& T& T& T& T& T\\ T& F& T& F& F& T& F& F& T& T\\ F& T& T& F& F& F& T& F& T& F\\ F& F& F& F& F& F& T& F& T& T\end{array}$
$\because$ The truth value of all the elements of the column $a\wedge (a\to b)\to b$ are true.
$\therefore a\wedge (a\to b)\to b$ is a tautology