The statement (p Rightarrow q) vee (p Rightar | vedclass

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Question

(B) Given statement: $(p$ $\Rightarrow q) \vee (p$ $\Rightarrow r)$Using the identity $(p \Rightarrow q) \equiv (\sim p \vee q)$:$= (\sim p \vee q) \v

Vedclass · Accepted Answer

$(\sim q) \Rightarrow ((\sim r) \vee p)$

Vedclass · Answer

(B) Given statement: $(p$ $\Rightarrow q) \vee (p$ $\Rightarrow r)$Using the identity $(p \Rightarrow q) \equiv (\sim p \vee q)$:$= (\sim p \vee q) \vee (\sim p \vee r)$$= \sim p \vee (q \vee r)$$= p \Rightarrow (q \vee r)$This matches option $(C)$.Now check other options:Option $(A): (p \wedge \sim r)$ $\Rightarrow q \equiv \sim(p \wedge \sim r) \vee q \equiv (\sim p \vee r) \vee q \equiv \sim p \vee (q \vee r) \equiv p$ $\Rightarrow (q \vee r)$. (Equivalent)Option $(D): (p \wedge \sim q)$ $\Rightarrow r \equiv \sim(p \wedge \sim q) \vee r \equiv (\sim p \vee q) \vee r \equiv \sim p \vee (q \vee r) \equiv p$ $\Rightarrow (q \vee r)$. (Equivalent)Option $(B): (\sim q)$ $\Rightarrow ((\sim r) \vee p) \equiv \sim(\sim q) \vee (\sim r \vee p) \equiv q \vee \sim r \vee p \equiv p \vee q \vee \sim r$. (Not equivalent to $p \Rightarrow (q \vee r)$).

The statement $(p$ $\Rightarrow q) \vee (p$ $\Rightarrow r)$ is $NOT$ equivalent to:

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