# Which of the following sentences are statements?

Question:

Which of the following sentences are statements? Justify

(i) A triangle has three sides.

(ii) 0 is a complex number.

(iii) Sky is red.

(iv) Every set is an infinite set.

(v) 15 + 8 > 23.

(vi) y + 9 = 7.

(viii) Every square is a rectangle.

(ix) Sum of opposite angles of a cyclic quadrilateral is 180°.

(x) Sin2x + cos2 x = 0

Solution:

(i) A triangle has three sides.

A statement is a declarative sentence if it is either true or false but not both.

So, the given sentence is true.

Hence, it is a true statement

(ii) 0 is a complex number.

A statement is a declarative sentence if it is either true or false but not both.

So, the given sentence “0 is a complex number” is true. Because we can write it as a+ib, where imaginary part is 0 as, a+0i.

Hence, it is a true statement

(iii) Sky is red.

A statement is a declarative sentence if it is either true or false but not both.

The given sentence “sky is Red” is false.

Hence, it is a false statement

(iv) Every set is an infinite set.

A statement is a declarative sentence if it is either true or false but not both.

The given sentence “Every set is an infinite set” is False.

Hence, it is a false statement

(v) 15 + 8 > 23.

A statement is a declarative sentence if it is either true or false but not both.

So, the given Expression “15 + 8 > 23” is false.

As the result of L.H.S will always equal to the result of R.H.S

Hence, it is a false statement

(vi) y + 9 = 7.

A statement is a declarative sentence if it is either true or false but not both.

Here, y + 9 = 7 will be true for some value and it will be false for some value.

Like, at y= -2, the given expression is true and Y=1 or any other value, the expression is false.

Hence, it is not a statement

A statement is a declarative sentence if it is either true or false but not both.

Here, the given sentence “Where is your bag” is a question.

Hence, it is not a statement

(viii) Every square is a rectangle.

A statement is a declarative sentence if it is either true or false but not both.

So, the given sentence “Every square is a rectangle.” is true.

Hence, it is a true statement

(ix) Sum of opposite angles of a cyclic quadrilateral is 180°.

A statement is a declarative sentence if it is either true or false but not both.

By the properties of quadrilateral “Sum of opposite angles of a cyclic quadrilateral is180°.”

So, the given sentence is true.

Hence, it is a statement

(x) Sin2x + cos2 x = 0

A statement is a declarative sentence if it is either true or false but not both.

According to the laws of trigonometry, sin2x + cos2x = 1

So, the given expression is False.

Hence, it is a false statement