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  • Which of the following sentences are statements? Justify i) A triangle has three sides.

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

vii) Where is your bag?

viii) Every square is a rectangle.

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

x) \sin ^{2}x+\cos ^{2}x=0

 

Answers (1)

i) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it shouldn’t be both.The given sentence is a true statement, since we know that it is true that “a triangle has three sides.”

ii) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both.The given sentence is a true statement, since we know that it is true that “0 is a complex number”, because we can also write it as a + ib, where the imaginary part is 0 as, a + 0i.

iii) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both. The given sentence is a false statement, since we know that it is not true that “sky is red.”

iv) Concept:

 A statement is considered as an assertive sentence if it is either true or false, but it should not be both.The given sentence is a false statement, since we know that it is not true that “every set is an infinite set.”

v) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both. The given sentence is a false statement, since we know that it is not true that 15 + 8 > 23 because LHS\neq RHS.

vi) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both.The given sentence is not a statement, since we know that “y + 9 = 7” will be true for some value & false for some. For example, at y = -2 is true & y = 1 or any other value is false.

vii) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both. The given sentence is not a statement since we know that “where is your bag” is a question.

viii) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it shouldn’t be both.Theve given sentence is a true statement, since we know that it is true that “ every square is a rectangle.”

ix) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both. The given sentence is a true statement, since we know that “Sum of opposite angles of a cyclic quadrilateral is 180?” is true by the properties f quadrilateral.

x) Concept:

A statement is considered as an assertive sentence if it is either true or false, but it should not be both. The given sentence is a false statement since we know that \sin ^{2}x+\cos^{2}x=1 is the correct expression according to the laws of trigonometry.

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