The negation of the converse of the statement | vedclass

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

Question

(A) $1$. The given statement is $p \lor q$. $2$. The converse of a statement $p \implies q$ is $q \implies p$. However, for a simple disjunction $p \l

Vedclass · Accepted Answer

$\sim p \land \sim q$

Vedclass · Answer

(A) $1$. The given statement is $p \lor q$. $2$. The converse of a statement $p \implies q$ is $q \implies p$. However, for a simple disjunction $p \lor q$, the converse is defined by swapping the components: $q \lor p$. $3$. Since $p \lor q$ is logically equivalent to $q \lor p$, the converse is $q \lor p$. $4$. The negation of the converse is $\sim(q \lor p)$. $5$. By De Morgan's Law, $\sim(q \lor p) \equiv \sim q \land \sim p$, which is equivalent to $\sim p \land \sim q$.

The negation of the converse of the statement $p \lor q$ is:

Similar Questions

For the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?

If $p$ and $q$ each have truth value $F$,then the truth values of the statement patterns $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$ and $\sim p \leftrightarrow (p \rightarrow \sim q)$ respectively are

Write the negation of the following statement:
$r:$ All birds have wings.

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.

The statement pattern $(p \vee q) \to \sim r$ is logically equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module