Question

If the Boolean expression $(p\wedge q)⊛(p\otimes q)$ is a tautology, then $⊛$ and $\otimes$ are respectively given by

• A. $\wedge ,\to$
• B. $\to ,\to$
• C. $\vee ,\to$
• D. $\wedge ,\vee$

Answer 1

The correct option is B $\to ,\to$

In $(p\wedge q)⊛(p\otimes q),$
$⊛$ cannot be $\wedge$ as $(p\wedge q)⊛(p\otimes q)$ cannot be tautology whenever $p\wedge q$ substatement is False.

So, from given options $(⊛,\otimes )$ can be $(\to ,\to )$ or $(\vee ,\to )$

$\begin{array}{cccccc}p& q& p\wedge q& p\to q& (⊛,\otimes )\equiv (\to ,\to )& (⊛,\otimes )\equiv (\vee ,\to )\\ & & & & (p\wedge q)⊛(p\otimes q)& (p\wedge q)⊛(p\otimes q)\\ T& T& T& T& T& T\\ T& F& F& F& T& F\\ F& T& F& T& T& T\\ F& F& F& T& T& T\end{array}$

$\therefore (⊛,\otimes )\equiv (\to ,\to )$