Q. 14.5( 30 Votes )

Which of the following sentences 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°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

Answer :

(i) Since there are 28 or 30 or 31 days in a month.


It is a false Sentence


Hence it is a statement.


(ii) Mathematics is difficult for some but not for other.


Hence this statement can be both true or false.


So it is not a statement.


(iii) 5+7 = 12 which is greater than 10


It is true


Hence it is a statement.


(iv) This sentence may be true or may not be.


For example 22 = 4(even)


32 = 9(odd)


Hence the square of a natural number may be even or may be odd.


Hence this is not a statement.


(v) Square is quadrilateral & has equal length (all four sides are equal). But, trapezium is quadrilateral which has unequal length.


(Only two sides are equal)


Thus, Sentence is sometimes true & sometimes false.


Hence it is not a statement.


(vi) Since it is order.


Hence it is not a statement.


(vii) It is false sentence.


Because product of (-1) & 8 is -8.


Hence it is a statement.


(viii) This Sentence is always true.


Because the sum of interior angles of a triangle is 180°.


Hence it is a statement.


(ix) It is not clear which day is windy day.


So, it may be true or maybe false.


Hence it is not a statement.


(x) All real numbers can be written in the form of


a + i0 (when 'a' is real number)


So, all real numbers are complex numbers


Hence, it is always true.


Hence it is a statement.


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