Question

(i)Which of the following sentences are statements. Give reasons for your answer
There are $35$ days in a month

(ii)Which of the following sentences are statements. Give reasons for your answer
Mathematics is difficult

(iii)Which of the following sentences are statements. Give reasons for your answer
The sum of $5$ and $7$ is greater than $10$

(iv)Which of the following sentences are statements. Give reasons for your answer
The square of number is even number

(v)Which of the following sentences are statements. Give reasons for your answer
The sides of a quadrilateral have equal length

(vi)Which of the following sentences are statements. Give reasons for your answer
Answer this question

(vii)Which of the following sentences are statements. Give reasons for your answer
The product of $(-1)\text{and}8\text{is}8$

(viii)Which of the following sentences are statements. Give reasons for your answer
The sum of all interior angles of a triangle is ${180}^{\circ }$

(ix)Which of the following sentences are statements. Give reasons for your answer
Today is windy day

(x)Which of the following sentences are statements. Give reasons for your answer
All real numbers are complex numbers

Answer 1

(i) Given sentence : There are $35$ days in a monthIt is a false sentence.
Reason: There are $28\text{or}30\text{or}31$ days in a month.
Hence, it is a Statement

(ii) Given sentence : Mathematics is difficult
This sentence can be both true or false.
Reason: Mathematics is difficult for some but not for others.
Hence, it’s not a Statement

(iii) Given sentence : The sum of $5\text{and}7$ is greater than $10$
It is a true sentence.
Reason: The sum of $5\text{and}7\text{is}5+7=12$,
which is always greater than $10$.
Hence, it’s a Statement

(iv) Given sentence : The square of number is even number
This sentence may or may not be true.
Reason: For example: square of $4$ is $4^2=16$ and square of $5$ is $5^2=25$
Thus, square of a number may be even or may be odd.
Hence, it’s not a Statement

(v)Given sentence : The sides of a quadrilateral have equal length.
This sentence may or may not be true.
Reason: Square is a quadrilateral having all four equal sides, but trapezium is a quadrilateral having unequal lengths of sides.
Hence, it’s not a Statement

(vi) Given sentence : Answer this question
This sentence is not a statement.
Reason: This sentence is an order.

(vii) Given sentence : The product of $(-1)\text{and}8\text{is}8$
This sentence is false.
Reason: Product of $(-1)\text{and}8$ is equal to $-8$
Hence, it is a Statement

(viii) Given sentence : The sum of all interior angles of a triangle is ${180}^{\circ }$
This sentence is always true.
Reason: The sum of all interior angles of a triangle is always ${180}^{\circ }$.
Hence, it is a Statement

(ix) Given sentence : Today is windy day.
This sentence may be true or may be false.
Reason: We don’t know which day is windy day.
Hence, it’s not a Statement

(x)Given sentence : All real numbers are complex numbers
This sentence is always true.
Reason: All real numbers can be written in the form of $a+ib$. where a is real number and $b$ is zero. So, all real number can be written in the form of complex number.
$\therefore$ All real number are complex numbers
Hence, it’s a Statement