Which one of the following statements is not | vedclass

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(B) tautology is a statement that is always true for all possible truth values of its components.Check option $(A): (p \vee q) 	o (p \vee (\sim q))$$

Vedclass · Accepted Answer

$(p \vee q) 	o p$

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(B) tautology is a statement that is always true for all possible truth values of its components.Check option $(A): (p \vee q) 	o (p \vee (\sim q))$$= \sim (p \vee q) \vee (p \vee \sim q)$$= (\sim p \wedge \sim q) \vee (p \vee \sim q)$$= (\sim p \vee p \vee \sim q) \wedge (\sim q \vee p \vee \sim q)$$= T \wedge (p \vee \sim q) = p \vee \sim q$. This is not a tautology.Check option $(B): (p \vee q) 	o p$$= \sim (p \vee q) \vee p = (\sim p \wedge \sim q) \vee p$$= (\sim p \vee p) \wedge (\sim q \vee p) = T \wedge (\sim q \vee p) = \sim q \vee p$. This is not a tautology.Check option $(C): p 	o (p \vee q)$$= \sim p \vee (p \vee q) = (\sim p \vee p) \vee q = T \vee q = T$. This is a tautology.Check option $(D): (p \wedge q) 	o ((\sim p) \vee q)$$= \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.Note: Both $(A)$ and $(B)$ are not tautologies. However,in standard examination contexts for this specific question,$(B)$ is often the intended answer as it is a common logical fallacy.

Which one of the following statements is not a tautology?

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