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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$I$) If $1$ is not a prime number, then $2$ is not a prime number.
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$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
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