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

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Question

(C) We test the possible combinations for $(\oplus, \Theta)$ where $\oplus, \Theta \in \{\wedge, \vee\}$.Case $1$: $(\oplus, \Theta) = (\wedge, \vee)$

Vedclass · Accepted Answer

$(\wedge, \vee)$

Vedclass · Answer

(C) We test the possible combinations for $(\oplus, \Theta)$ where $\oplus, \Theta \in \{\wedge, \vee\}$.Case $1$: $(\oplus, \Theta) = (\wedge, \vee)$$(p \wedge q) \wedge (\sim p \vee q) \equiv (p \wedge q \wedge \sim p) \vee (p \wedge q \wedge q)$$\equiv (F \wedge q) \vee (p \wedge q) \equiv F \vee (p \wedge q) \equiv p \wedge q$.This matches the given expression.Case $2$: $(\oplus, \Theta) = (\wedge, \wedge)$$(p \wedge q) \wedge (\sim p \wedge q) \equiv (p \wedge \sim p) \wedge q \equiv F \wedge q \equiv F$.Case $3$: $(\oplus, \Theta) = (\vee, \vee)$$(p \vee q) \wedge (\sim p \vee q) \equiv (p \wedge \sim p) \vee q \equiv F \vee q \equiv q$.Case $4$: $(\oplus, \Theta) = (\vee, \wedge)$$(p \vee q) \wedge (\sim p \wedge q) \equiv (p \wedge \sim p \wedge q) \vee (q \wedge \sim p \wedge q) \equiv F \vee (q \wedge \sim p) \equiv q \wedge \sim p$.Thus,the correct ordered pair is $(\wedge, \vee)$.

If the Boolean expression $(p \oplus q) \wedge (\sim p \Theta q)$ is equivalent to $p \wedge q$,where $\oplus, \Theta \in \{\wedge, \vee\}$,then the ordered pair $(\oplus, \Theta)$ is:

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