Which of the following sentences are statements? Give reasons for your answer.
(v) The sides of a quadrilateral have equal lengths.
(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.
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(i) The maximum number of days in a month is 31, so this sentence is incorrect. Therefore, it is a statement.
(ii) This sentence is subjective. For some people, Mathematics can be easy, and for some others, it can be difficult. Therefore, it is not a statement.
(iii) The sum of 5 and 7 is 12, and it is greater than 10. Therefore, this sentence is always correct. Hence, it is a statement.
(iv) This sentence can sometimes be correct and sometimes incorrect. For example, the square of 2 is an even number, but the square of 3 is an odd number. Hence, it is not a statement
(v) This sentence can sometimes be correct and sometimes incorrect. For example, squares and rhombi have sides of equal lengths, whereas trapezia and rectangles have sides of unequal lengths. Therefore, it is not a statement.
(vi) It is an order. Hence, it is not a statement.
(vii) The given sentence is incorrect because the product of (-1) and 8 is – 8. Hence, it is a statement.
(viii) The given sentence is correct, and therefore, it is a statement.
(ix) The given sentence is not a statement because the day that is being referred to is not evident from the sentence.
(x) The given sentence is always correct because all real numbers can be written as a × 1 + 0 × i. Hence, it is a statement.