Which of the following logical statements is | vedclass

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(A) Step $1$: $A$ tautology is a statement that is true for all possible truth values of its components.Step $2$: Analyze option $(A)$: $[(p 	o q) \l

Vedclass · Accepted Answer

$[(p 	o q) \land \sim q] 	o \sim p$

Vedclass · Answer

(A) Step $1$: $A$ tautology is a statement that is true for all possible truth values of its components.Step $2$: Analyze option $(A)$: $[(p 	o q) \land \sim q] 	o \sim p$. Step $3$: Construct the truth table for $[(p 	o q) \land \sim q] 	o \sim p$:- If $p=T, q=T$: $[(T 	o T) \land F] 	o F \implies [T \land F] 	o F \implies F 	o F = T$.- If $p=T, q=F$: $[(T 	o F) \land T] 	o F \implies [F \land T] 	o F \implies F 	o F = T$.- If $p=F, q=T$: $[(F 	o T) \land F] 	o T \implies [T \land F] 	o T \implies F 	o T = T$.- If $p=F, q=F$: $[(F 	o F) \land T] 	o T \implies [T \land T] 	o T \implies T 	o T = T$.Step $4$: Since all truth values are $T$, the statement is a tautology.

Which of the following logical statements is a tautology?

Similar Questions

Among the statements:
$(S1) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow ( p$ $\Rightarrow r )$
$(S2) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow (( p$ $\Rightarrow r ) \vee ( q$ $\Rightarrow r ))$

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

The statement $p \to (q \to p)$ is equivalent to

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :

If the statement $p \leftrightarrow (q \rightarrow p)$ is false,then the true statement/statement pattern is

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