If p, q and r are three propositions,then whi | vedclass

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

Question

(C) conditional statement $A \rightarrow B$ is false only when $A$ is True and $B$ is False.Let $A = (p \vee q) \wedge ((\sim p) \vee r)$ and $B = ((\

Vedclass · Accepted Answer

$p = F, q = T, r = F$

Vedclass · Answer

(C) conditional statement $A \rightarrow B$ is false only when $A$ is True and $B$ is False.Let $A = (p \vee q) \wedge ((\sim p) \vee r)$ and $B = ((\sim q) \vee r)$.We need to find the case where $A = T$ and $B = F$.For $B = ((\sim q) \vee r)$ to be False,both $(\sim q)$ and $r$ must be False.This implies $q = T$ and $r = F$.Now,substitute $q = T$ and $r = F$ into $A = (p \vee q) \wedge ((\sim p) \vee r)$:$A = (p \vee T) \wedge ((\sim p) \vee F)$$A = T \wedge (\sim p)$For $A$ to be True,$(\sim p)$ must be True,which means $p = F$.Thus,the combination $p = F, q = T, r = F$ makes the expression False.

If $p, q$ and $r$ are three propositions,then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \rightarrow ((\sim q) \vee r)$ false?

Similar Questions

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to

For the statement: "If a quadrilateral $ABCD$ is a rhombus,then its opposite sides are parallel",its contrapositive and converse are respectively given by:

The expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to

State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
To apply for a driving licence,you should have a ration card or a passport.

Negation of the statement: $\sqrt{5}$ is an integer or $5$ is irrational is

Vedclass Test Series

Exam Paper Generator

Online Exam Module