The statement (p wedge q) Rightarrow (p wedge | vedclass

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

Question

(D) Given statement: $(p \wedge q) \Rightarrow (p \wedge r)$Using the logical equivalence $A \Rightarrow B \equiv \sim A \vee B$:$\sim(p \wedge q) \ve

Vedclass · Accepted Answer

$(p \wedge q) \Rightarrow r$

Vedclass · Answer

(D) Given statement: $(p \wedge q) \Rightarrow (p \wedge r)$Using the logical equivalence $A \Rightarrow B \equiv \sim A \vee B$:$\sim(p \wedge q) \vee (p \wedge r)$Apply De Morgan's Law:$(\sim p \vee \sim q) \vee (p \wedge r)$Using the distributive law $(\sim p \vee \sim q) \vee (p \wedge r) \equiv ((\sim p \vee \sim q) \vee p) \wedge ((\sim p \vee \sim q) \vee r)$:$((\sim p \vee p) \vee \sim q) \wedge (\sim p \vee \sim q \vee r)$Since $(\sim p \vee p) \equiv T$ (Tautology):$(T \vee \sim q) \wedge (\sim p \vee \sim q \vee r)$$T \wedge (\sim p \vee \sim q \vee r) \equiv \sim p \vee \sim q \vee r$Rearranging the terms:$(\sim p \vee \sim q) \vee r$Using De Morgan's Law again:$\sim(p \wedge q) \vee r$Converting back to implication:$(p \wedge q) \Rightarrow r$

The statement $(p \wedge q) \Rightarrow (p \wedge r)$ is equivalent to:

Similar Questions

The inverse of the statement "If the surface area increases,then the pressure decreases." is

Which of the following is not a correct statement?

The statement pattern $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ is equivalent to

Which of the following statements is $NOT$ logically equivalent to $(p \to \sim p) \to (p \to q)$?

If the truth value of the statement pattern $( \sim p \land q) \lor ( \sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module