The contrapositive of the inverse of p righta | vedclass

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

Question

(B) The inverse of a conditional statement $A \rightarrow B$ is $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (p$ $\rightarrow q)$,t

Vedclass · Accepted Answer

$(\sim p \vee q) \rightarrow p$

Vedclass · Answer

(B) The inverse of a conditional statement $A \rightarrow B$ is $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (p$ $\rightarrow q)$,the inverse is $\sim p$ $\rightarrow \sim (p$ $\rightarrow q)$. The contrapositive of a conditional statement $A \rightarrow B$ is $\sim B \rightarrow \sim A$. Applying this to the inverse $\sim p$ $\rightarrow \sim (p$ $\rightarrow q)$,we get: $\sim [\sim (p$ $\rightarrow q)]$ $\rightarrow \sim (\sim p)$ $= (p$ $\rightarrow q)$ $\rightarrow p$ Since $p \rightarrow q \equiv \sim p \vee q$,the expression becomes $(\sim p \vee q) \rightarrow p$.

The contrapositive of the inverse of $p$ $\rightarrow (p$ $\rightarrow q)$ is

Similar Questions

Which of the following is an open statement?

The contrapositive of $\sim q \to p$ is equivalent to

The truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of $(\sim p \vee q) \rightarrow (p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow (\sim p \wedge q)$ are respectively:

The negation of the proposition "If $2$ is prime,then $3$ is odd" is:

If the symbolic form of the switching circuit is $[\sim p \vee (p \wedge \sim q)] \vee q$,then the current flows through the circuit only if

Vedclass Test Series

Exam Paper Generator

Online Exam Module