Question

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 1

(i)

The given sentence is: there are 35 days in a month. Since the maximum number of days in a month is 31, thus the given sentence is incorrect. Also, the sentence is said to be a statement when it is mathematically correct and if it is either true or false but not both. As the given sentence is false, thus it is a statement.

(ii)

The given sentence is: mathematics is difficult. For some people, mathematics is a difficult subject but for other people, it is a very easy subject, thus the sentence is subjective. As the given sentence is true as well as false, thus it is not a statement.

(iii)

The given sentence is: The sum of 5 and 7 is greater than 10. Since the sum of 5 and 7 is 12 which is greater than 10, thus the sentence is true. As the given sentence is true, thus it is a statement.

(iv)

The given sentence is: The square of a number is an even number. Since the square of 2 is 4 that is an even number while the square of 3 is 9 which is an odd number, thus the sentence is true for some numbers but false for other numbers. As the given sentence is true as well as false, thus it is not a statement.

(v)

The given sentence is: The sides of a quadrilateral have equal length. The quadrilaterals such as square and rhombus have sides with equal lengths while quadrilaterals such as rectangle and trapezium have sides with unequal lengths. Therefore, the sentence is true for some quadrilaterals while for some quadrilaterals, it is false. As the sentence is true as well as false, thus it is not a statement.

(vi)

The given sentence is: Answer this question. Since the sentence is an order to someone and is not considered as a mathematical language, thus it is not a statement.

(vii)

The given sentence is: The product of ( −1 ) and 8 is 8. Since the product of ( −1 ) and 8 is ( −8 ) , thus the sentence is false. As the sentence is incorrect, thus it is a statement.

(viii)

The given sentence is: The sum of all interior angles of a triangle is 180° . Since the sum of all interior angles of a triangle is 180° , thus the sentence is correct. As the sentence is true, thus it is a statement.

(ix)

The given sentence is: Today is a windy day. Since the sentence contains variable time i.e. today, thus it is not a statement.

(x)

The given sentence is: All real numbers are complex numbers. Since all real numbers can be written in the form of complex numbers i.e. a×1+0×i , thus the sentence is true. As the given sentence is correct, thus it is a statement.