Consider the following statements:P : Ramu is | vedclass

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

Question

(D) Given statements:$P$: Ramu is intelligent$Q$: Ramu is rich$R$: Ramu is not honestThe statement "Ramu is intelligent and honest if and only if Ramu

Vedclass · Accepted Answer

$((P \wedge (\sim R)) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \vee R))$

Vedclass · Answer

(D) Given statements:$P$: Ramu is intelligent$Q$: Ramu is rich$R$: Ramu is not honestThe statement "Ramu is intelligent and honest if and only if Ramu is not rich" is represented as $(P \wedge \sim R) \Leftrightarrow \sim Q$.The negation of the statement is $\sim[(P \wedge \sim R) \Leftrightarrow \sim Q]$.Using the identity $\sim(A \Leftrightarrow B) \equiv (A \wedge \sim B) \vee (B \wedge \sim A)$,where $A = (P \wedge \sim R)$ and $B = \sim Q$:$= ((P \wedge \sim R) \wedge \sim(\sim Q)) \vee (\sim Q \wedge \sim(P \wedge \sim R))$$= ((P \wedge \sim R) \wedge Q) \vee (\sim Q \wedge (\sim P \vee \sim(\sim R)))$$= ((P \wedge \sim R) \wedge Q) \vee (\sim Q \wedge (\sim P \vee R))$Thus,the correct option is $D$.

Consider the following statements:
$P :$ Ramu is intelligent
$Q :$ Ramu is rich
$R :$ Ramu is not honest
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

Similar Questions

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

The last column in the truth table of the statement pattern $[p \rightarrow (q \wedge \sim p)] \vee [(p \vee \sim q) \wedge p]$ is

$\sim (p \vee (\sim q))$ is equal to .......

The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ is logically equivalent to

Write the negation of the following statement:
$r:$ For every real number $x$,either $x > 1$ or $x < 1.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the following statements:$P :$ Ramu is intelligent$Q :$ Ramu is rich$R :$ Ramu is not honestThe negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as: