The negation of the statement (( A wedge ( B | vedclass

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

Question

(A) Let $p = (( A \wedge ( B \vee C ))$ $\Rightarrow ( A \vee B ))$ $\Rightarrow A$. Using the implication rule $X \Rightarrow Y \equiv \sim X \vee Y$

Vedclass · Accepted Answer

equivalent to $\sim A$

Vedclass · Answer

(A) Let $p = (( A \wedge ( B \vee C ))$ $\Rightarrow ( A \vee B ))$ $\Rightarrow A$. Using the implication rule $X \Rightarrow Y \equiv \sim X \vee Y$,we have: $p \equiv \sim (( A \wedge ( B \vee C )) \Rightarrow ( A \vee B )) \vee A$. Applying the negation rule $\sim (X \Rightarrow Y) \equiv X \wedge \sim Y$: $p \equiv (( A \wedge ( B \vee C )) \wedge \sim ( A \vee B )) \vee A$. Using De Morgan's Law $\sim ( A \vee B ) \equiv \sim A \wedge \sim B$: $p \equiv (( A \wedge ( B \vee C )) \wedge ( \sim A \wedge \sim B )) \vee A$. Since $( A \wedge \sim A ) \equiv F$ (False),the expression simplifies to: $p \equiv ( F \wedge ( B \vee C ) \wedge \sim B ) \vee A \equiv F \vee A \equiv A$. Therefore,the negation of the statement is $\sim p \equiv \sim A$.

The negation of the statement $(( A \wedge ( B \vee C ))$ $\Rightarrow ( A \vee B ))$ $\Rightarrow A$ is

Similar Questions

Which of the following statements is logically equivalent to $∼ (p \leftrightarrow q)$?

By giving a counterexample,show that the following statement is false: "If $n$ is an odd integer,then $n$ is prime."

Which of the following logical statements is a tautology?

The negation of the proposition "If $2$ is prime,then $3$ is odd" is:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module