The statement B Rightarrow ((sim A) vee B) is | vedclass

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(C) The given statement is $B \Rightarrow ((\sim A) \vee B)$.Using the logical equivalence $P \Rightarrow Q \equiv (\sim P) \vee Q$,we have:$B \Righta

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$A$ $\Rightarrow ((\sim A)$ $\Rightarrow B)$

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(C) The given statement is $B \Rightarrow ((\sim A) \vee B)$.Using the logical equivalence $P \Rightarrow Q \equiv (\sim P) \vee Q$,we have:$B \Rightarrow ((\sim A) \vee B) \equiv (\sim B) \vee ((\sim A) \vee B)$By the commutative and associative laws:$(\sim B) \vee B \vee (\sim A) \equiv T \vee (\sim A) \equiv T$Since the statement is a tautology,we check the options for tautologies.Option $C$ is $A$ $\Rightarrow ((\sim A)$ $\Rightarrow B) \equiv (\sim A) \vee ((\sim A)$ $\Rightarrow B) \equiv (\sim A) \vee (A \vee B) \equiv (\sim A \vee A) \vee B \equiv T \vee B \equiv T$.Thus,the statement is equivalent to $A$ $\Rightarrow ((\sim A)$ $\Rightarrow B)$.

The statement $B \Rightarrow ((\sim A) \vee B)$ is equivalent to

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