If the Boolean expression (p wedge q) circled | vedclass

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(A) We test the options to see which expression results in a tautology $(t)$:Option $A$: $(p \wedge q)$ $\rightarrow (p$ $\rightarrow q)$$= \sim(p \we

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$\rightarrow,$ $\rightarrow$

Vedclass · Answer

(A) We test the options to see which expression results in a tautology $(t)$:Option $A$: $(p \wedge q)$ $\rightarrow (p$ $\rightarrow q)$$= \sim(p \wedge q) \vee (\sim p \vee q)$$= (\sim p \vee \sim q) \vee (\sim p \vee q)$$= \sim p \vee (\sim q \vee q)$$= \sim p \vee t$$= t$ (This is a tautology).Option $B$: $(p \wedge q) \wedge (p \vee q) = (p \wedge q)$ (Not a tautology).Option $C$: $(p \wedge q) \vee (p \rightarrow q) = (p \wedge q) \vee (\sim p \vee q) = \sim p \vee q$ (Not a tautology).Option $D$: $(p \wedge q) \wedge (p \rightarrow q) = (p \wedge q) \wedge (\sim p \vee q) = p \wedge q$ (Not a tautology).Thus,the correct option is $A$.

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

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