Which of the following logical equivalences is true?
- A$p$ $\Rightarrow q \equiv \sim p$ $\Rightarrow \sim q$
- B$\sim (p \Rightarrow \sim q) \equiv \sim p \wedge q$
- C$\sim (\sim p \Rightarrow \sim q) \equiv \sim p \wedge q$
- D$\sim (p \Leftrightarrow q) \equiv [\sim (p$ $\Rightarrow q) \wedge \sim (q$ $\Rightarrow p)]$
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Similar Questions
Are the following pairs of statements negations of each other:
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.
Easy
View Solution$(p \wedge \sim q) \wedge (\sim p \vee q)$ is :-
The statement $B \Rightarrow ((\sim A) \vee B)$ is equivalent to
DifficultJEE MAIN 2023
View SolutionFor the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
Consider the following three statements:
$(A)$ If $3+3=7$ then $4+3=8$.
$(B)$ If $5+3=8$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$.
Which of the following statements is correct?
$(A)$ If $3+3=7$ then $4+3=8$.
$(B)$ If $5+3=8$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$.
Which of the following statements is correct?
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