Let r in {p, q, sim p, sim q} be such that th | vedclass

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(C) To determine which $r$ makes the statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ a tautology,we test each option using a truth table.F

Vedclass · Accepted Answer

$\sim p$

Vedclass · Answer

(C) To determine which $r$ makes the statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ a tautology,we test each option using a truth table.For $r = \sim p$:The statement becomes $(\sim p \vee \sim p) \Rightarrow (p \wedge q) \vee \sim p$.This simplifies to $\sim p \Rightarrow (p \wedge q) \vee \sim p$.Using the law of absorption,$(p \wedge q) \vee \sim p$ is equivalent to $(\sim p \vee p) \wedge (\sim p \vee q)$,which is $T \wedge (\sim p \vee q) = \sim p \vee q$.So the statement is $\sim p \Rightarrow (\sim p \vee q)$.Since $\sim p \Rightarrow (\sim p \vee q)$ is equivalent to $
eg(\sim p) \vee (\sim p \vee q) = p \vee \sim p \vee q = T \vee q = T$,the statement is a tautology.Thus,$r = \sim p$ is the correct option.

Let $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to

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