Q.Give three examples of sentences which are not statements. Give reasons for the answers.

A sentence qualifies as a mathematical statement only if it is either true or false, but never both and never neither. This single test rules out a whole range of familiar sentence types: exclamations ("How beautiful!"), commands ("Open the door"), and questions ("Where are you going?") assert nothing that can be judged true or false, so none of them are statements. Sentences carrying an opinion ("Women are more intelligent than men") fail too, because reasonable people can disagree with no way to settle the matter. Sentences with a free, unfixed variable — "The sum of x and y is greater than 0" — are also excluded, since their truth depends on values we haven't been told; quantifying the variable ("for any natural numbers x and y...") turns such a sentence into a genuine statement. Sentences that shift meaning with variable time, place, or an unspecified pronoun ("Tomorrow is Friday", "She is a mathematics graduate", "Kashmir is far from here") are likewise not statements, because their truth value would change depending on when or by whom they are spoken. A statement can still be false — "There are 40 days in a month" is a statement precisely because it is always false, never sometimes true. Statements are conventionally labelled with small letters p, q, r, and so on.