Write the negation of the following statement:
Both the diagonals of a rectangle have the same length.
Both the diagonals of a rectangle have the same length.
(N/A) The given statement is: $P$: Both the diagonals of a rectangle have the same length.
The negation of a statement $P$ is denoted by $\sim P$.
The negation of the statement "Both the diagonals of a rectangle have the same length" is:
"It is false that both the diagonals of a rectangle have the same length."
Alternatively,this can be written as:
"There exists at least one rectangle whose diagonals do not have the same length."
The negation of a statement $P$ is denoted by $\sim P$.
The negation of the statement "Both the diagonals of a rectangle have the same length" is:
"It is false that both the diagonals of a rectangle have the same length."
Alternatively,this can be written as:
"There exists at least one rectangle whose diagonals do not have the same length."
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Similar Questions
The given circuit is equivalent to:
Which one of the following is the pair of equivalent circuits?
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
Which of the following statements has the truth value $T$?
$A$: Cube roots of unity are in Geometric Progression and their sum is $0$.
$B$: $4+7 > 10$ iff $2+8 < 10$.
$C$: $\exists x \in N$ such that $x^2-3x+2=0$ and $\exists n \in N$ such that $n$ is an odd number.
$D$: $3+i$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$.
$A$: Cube roots of unity are in Geometric Progression and their sum is $0$.
$B$: $4+7 > 10$ iff $2+8 < 10$.
$C$: $\exists x \in N$ such that $x^2-3x+2=0$ and $\exists n \in N$ such that $n$ is an odd number.
$D$: $3+i$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$.
If $p : 5$ is not greater than $2$ and $q : \text{Jaipur is the capital of Rajasthan}$ are two statements,then the negation of the statement $p \Rightarrow q$ is:
Which of the following statements is a tautology?
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