If the truth value of the Boolean expression | vedclass

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

Question

(C) The implication $A \rightarrow B$ is false if and only if $A$ is true and $B$ is false. Here,$A = (p \vee q) \wedge (q \rightarrow r) \wedge (\sim

Vedclass · Accepted Answer

$T, F, F$

Vedclass · Answer

(C) The implication $A \rightarrow B$ is false if and only if $A$ is true and $B$ is false. Here,$A = (p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)$ and $B = (p \wedge q)$. For $B = (p \wedge q)$ to be false,at least one of $p$ or $q$ must be false. For $A$ to be true,all components $(p \vee q)$,$(q \rightarrow r)$,and $(\sim r)$ must be true. Since $(\sim r)$ is true,$r$ must be false. Since $(q \rightarrow r)$ is true and $r$ is false,$q$ must be false. Since $(p \vee q)$ is true and $q$ is false,$p$ must be true. Thus,the truth values are $p=T, q=F, r=F$. Checking option $C$: $p=T, q=F, r=F$ gives $A = (T \vee F) \wedge (F \rightarrow F) \wedge (\sim F) = T \wedge T \wedge T = T$ and $B = (T \wedge F) = F$. Since $T \rightarrow F$ is false,option $C$ is correct.

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be:

Similar Questions

Check the validity of the statement given below by the method specified against it.
$q:$ If $n$ is a real number with $n > 3$,then $n^{2} > 9$ (by contradiction method).

Which of the following Boolean expressions is not a tautology?

Consider the following statements:
$P$: Suman is brilliant
$Q$: Suman is rich
$R$: Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as:

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

In a Boolean Algebra $B$,for all $x, y \in B$,$x \wedge (x \vee y)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module