Which of the following sentences are statements? Give reasons for your answer.
"The sides of a quadrilateral have equal length."
"The sides of a quadrilateral have equal length."
(N/A) sentence is considered a statement in mathematical logic if it is either always true or always false.
The given sentence,"The sides of a quadrilateral have equal length," is ambiguous because its truth value depends on the specific type of quadrilateral.
For example,in a square or a rhombus,all sides are equal,making the statement true.
However,in a rectangle or a trapezium,the sides are not necessarily equal,making the statement false.
Since the sentence can be true or false depending on the context,it is not a mathematical statement.
The given sentence,"The sides of a quadrilateral have equal length," is ambiguous because its truth value depends on the specific type of quadrilateral.
For example,in a square or a rhombus,all sides are equal,making the statement true.
However,in a rectangle or a trapezium,the sides are not necessarily equal,making the statement false.
Since the sentence can be true or false depending on the context,it is not a mathematical statement.
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Similar Questions
Consider the following statements:
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.
State the converse and contrapositive of the following statement:
$r:$ If it is hot outside,then you feel thirsty.
$r:$ If it is hot outside,then you feel thirsty.
Easy
View SolutionIf $p: \forall n \in N, n^2+n$ is an even number and $q: \forall n \in N, n^2-n$ is an odd number,then the truth values of $p \wedge q, p \vee q$ and $p \rightarrow q$ are respectively:
Find the component statements of the following compound statement and check whether they are true or false.
Number $3$ is prime or it is odd.
Number $3$ is prime or it is odd.
Easy
View SolutionThe 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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