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 ${180}^{\circ }$
(ix) Today is a windy day
(x) All real numbers are complex numbers

Answer 1

(i) This sentence is incorrect because the maximum number of days in a month is $31$, hence it is a statement
(ii) This sentence is subjective in the sense that for some people, mathematics can be easy and for some others it can be difficult, hence it is not a statement
(iii) The sum of $5$ and $7$ is $12$ which is greater than $10$ Therefore this sentence is always correct, hence it is a statement
(iv) This sentence is sometimes correct and sometimes incorrect. For example the square of $2$ is an even number However the square of $3$ is an odd number, hence it is not a statement
(v) This sentence is sometimes correct and sometimes incorrect for example squares and rhombus have sides of equal lengths however trapezium and rectangles have sides of unequal lengths, hence it is not a statement
(vi) It is an order therefore it is not a statement
(vii) The product of $(-1)$ and 8 is $(-8)$ therefore the given sentence is incorrect, hence it is a statement
(viii) This sentence is correct and hence it is a statement
(ix) The day that is being referred to is not evident from the sentence, hence it is not a statement
(x) All real numbers can be written as $a\times 1+0\times i$ Therefore the given sentence is always correct, hence it is a statement