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 2^{2} = 4(even)

3^{2} = 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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