Question

How many of the following sentences are true statements
$\left(1\right)$ Paris is in France.
$\left(2\right)$ Each prime number has exactly two factors.
$\left(3\right)$ The equation $x^2+5|x|+6=0$ has no real roots.
$\left(4\right)(2+\sqrt{3})$ is a complex number.
$\left(5\right)$ Is $6$ a positive integer $?$
$\left(6\right)$ The product of $-3$ and $-2$ is $-6$.
$\left(7\right)$ The angles opposite to equal sides of an isosceles triangle are equal
$\left(8\right)$ Oh! it is too hot.
$\left(9\right)$ Monika is a beautiful girl.
$\left(10\right)$ Every quadratic equation has at least one real root.

Answer 1

Note: A sentence is called a mathematically acceptable statement if it is either true or false but not both.

$\left(1\right)$ The sentence ‘Paris is in France’ is a statement as Paris is located in France,
So the given sentence is true.

$\left(2\right)$ The sentence ‘Each prime number has exactly two factors’ is a true statement. It is a mathematically proven fact that each prime number has exactly two factors,1 and the number itself.

$\left(3\right)x^2+|5|x+6=0\Rightarrow |x{|}^2+5|x|+6=0$
$|x|=-2,-3$ that is not possible,
So it a true statement.

$\left(4\right)$ The number $2+\sqrt{3}$ can be expressed as $2+\sqrt{3}$ $+0i$. So it is is a complex number whose imaginary part is $0$

$\left(5\right)$ The sentence ‘Is $6$ a positive integer?’ is a question, so it is not a statement.

$\left(6\right)$ The sentence ‘The product of $-3$ and $-2$ is $-6$’ is a statement.
But, the product of $-3$ and $-2$ not $-6$. So the given sentence is false.

$\left(7\right)$It is mathematically proven that the angles opposite to the equal sides of an isosceles triangle are equal. So the given sentence is true, and it is a statement.

$\left(8\right)$ The sentence ‘Oh! It is too hot’ is not a statement. It is an exclamation.

$\left(9\right)$ The sentence ‘Monica is a beautiful girl’ is not a statement. The given sentence is an opinion; this can be true for some cases, false for some other case.

$\left(10\right)$ The given sentence is a false statement.
Because not every quadratic equation will have a real root.