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

Consider the following statements:
$r$: If $p \to q$ is false then $p \lor q$ is false.
$s$: If $p \leftrightarrow q$ is false then $p \lor q$ is false.
The truth values of $r \to s$ and $s \to r$ are respectively . . . . . .

Write the negation of the following statement:
Both the diagonals of a rectangle have the same length.

The compound statement $p \wedge (\sim p \wedge q)$ is

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....

The contrapositive of the statement "If it is raining,then $I$ will not come" is

Vedclass Test Series

Exam Paper Generator

Online Exam Module