Negation of the statement: $\sqrt{5}$ is an integer or $5$ is irrational is
- A$\sqrt{5}$ is an integer or $5$ is irrational
- B$\sqrt{5}$ is not an integer and $5$ is not irrational
- C$\sqrt{5}$ is an integer and $5$ is irrational
- D$\sqrt{5}$ is not an integer or $5$ is not irrational
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If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...
DifficultMHT CET 2026
View SolutionConsider the following statements:
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as:
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as:
For 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?
Which of the following sentences are statements? Give reasons for your answer.
Mathematics is difficult.
Mathematics is difficult.
Easy
View Solution$\sim(\sim p \rightarrow q) \equiv$
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