Question

Which of the following setences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (-1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is ${180}^{\circ }$.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

Answer 1

(i) No month has 35 days. Thus the sentence is false declarative sentence. Hence it is a statement.

(ii) Here the correctness of the sentence depends upon the observer. It may be easy for someone and may be difficult for other one. Hence it is not a statement.

(iii) The sentence is true. Hence it is a statement.

(iv) Here the correctness of the sentence depends upon the number that is squared. Hence it is not a statement.

(v) This sentence is sometimes true and sometimes false. For example sides in squares and rhombuses have equal length whereas in a rectangle and trapezium, they have unequal length. Hence it is not a statement.

(vi) This sentence is an order. Hence it is not a statement.

(vii) The sentence is true. Hence it is a statement.

(viii) The sentence is false. Hence it is a statement.

(ix) It is not clear from the context which day is referred. Hence it is not a statement.

(x) The sentence is true because all real numbers can be written in the form $a+i\times 0$. Hence it is a statement.