Negation of the inverse of the following stat | vedclass

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

Question

(B) Let $S$ be the statement $(p \wedge q) \rightarrow (p \vee \sim q)$.The inverse of $S$ is $\sim(p \wedge q) \rightarrow \sim(p \vee \sim q)$.Using

Vedclass · Accepted Answer

$\sim q$

Vedclass · Answer

(B) Let $S$ be the statement $(p \wedge q) \rightarrow (p \vee \sim q)$.The inverse of $S$ is $\sim(p \wedge q) \rightarrow \sim(p \vee \sim q)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,the inverse is:$\sim[\sim(p \wedge q)] \vee \sim(p \vee \sim q)$$\equiv (p \wedge q) \vee (\sim p \wedge q)$ (By De Morgan's Law)$\equiv (q \wedge p) \vee (q \wedge \sim p)$ (By Commutative Law)$\equiv q \wedge (p \vee \sim p)$ (By Distributive Law)$\equiv q \wedge T$ (By Complement Law,where $T$ is a tautology)$\equiv q$ (By Identity Law).Now,the negation of the inverse is $\sim(q) = \sim q$.

Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is

Similar Questions

Which of the following statements is a tautology?

If $p$ and $q$ are true statements and $r$ and $s$ are false statements,then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(p \vee s) \leftrightarrow(q \wedge r)$ are respectively

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

Write the contrapositive and converse of the following statement:
If two lines are parallel,then they do not intersect in the same plane.

Which of the following statements is a tautology?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is

Similar Questions

Which of the following statements is a tautology?

If $p$ and $q$ are true statements and $r$ and $s$ are false statements,then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(p \vee s) \leftrightarrow(q \wedge r)$ are respectively

Among the two statements:$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

Write the contrapositive and converse of the following statement:If two lines are parallel,then they do not intersect in the same plane.

Which of the following statements is a tautology?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

Write the contrapositive and converse of the following statement:
If two lines are parallel,then they do not intersect in the same plane.