Write the negation of the following statement:
$s:$ There exists a number $x$ such that $0 < x < 1.$
$s:$ There exists a number $x$ such that $0 < x < 1.$
- AThere exists a number $x$ such that $x \le 0$ or $x \ge 1.$
- BFor all numbers $x$,$0 < x < 1.$
- CThere does not exist a number $x$ such that $0 < x < 1.$
- DFor all numbers $x$,$x \le 0$ or $x \ge 1.$
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Similar Questions
The Boolean expression $((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)$ is equivalent to
DifficultJEE MAIN 2019
View SolutionLet $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow (\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:
For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
To enter a country,you need a passport or a voter registration card.
To enter a country,you need a passport or a voter registration card.
Easy
View SolutionGiven the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:
The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
DifficultMHT CET 2026
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