ConsiderStatement-1: (p wedge sim q) wedge (s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$Since $(\sim q \rightarrow \sim p)$ is the contrapositive of $(p \ri

Vedclass · Accepted Answer

Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is not a correct explanation for Statement-$1$

Vedclass · Answer

(D) Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$Since $(\sim q \rightarrow \sim p)$ is the contrapositive of $(p \rightarrow q)$,they have the same truth values.Thus,$(p \rightarrow q) \leftrightarrow (p \rightarrow q)$ is always true,which means it is a tautology.So,Statement-$2$ is true.Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$Using the associative and commutative laws:$= (p \wedge \sim p) \wedge (\sim q \wedge q)$$= F \wedge F = F$Since the result is always false,it is a fallacy.So,Statement-$1$ is true.Both statements are true,and Statement-$2$ is not an explanation for Statement-$1$.

Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.

Similar Questions

Write the component statements of the following compound statement and check whether the compound statement is true or false.
$A$ line is straight and extends indefinitely in both directions.

The negation of the statement "If $I$ become a teacher,then $I$ will open a school" is:

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

Rewrite the following statement in the form "$p$ if and only if $q$":
For you to get an $A$ grade,it is necessary and sufficient that you do all the homework regularly.

If $P$ and $Q$ are two statements,then which of the following compound statements is a tautology?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

ConsiderStatement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.