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.
(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.