because it is not known what time is referred here. For example, the sentence Tomorrow is Friday MATHEMATICAL REASONING is not a statement. The sentence is correct (true) on a Thursday but not on other days. The same argument holds for sentences with pronouns unless a particular person is referred to and for variable places such as “here”, “there” etc., For example, the sentences She is a mathematics graduate.
Kashmir is far from here. are not statements. Here is another sentence There are days in a month. Would you call this a statement?
Note that the period mentioned in the sentence above is a “variable time” that is any of months. But we know that the sentence is always false (irrespective of the month) since the maximum number of days in a month can never exceed . Therefore, this sentence is a statement. So, what makes a sentence a statement is the fact that the sentence is either true or false but not both.
While dealing with statements, we usually denote them by small letters p , q , r, ... For example, we denote the statement “ Fire is always hot ” by p . This is also written as p : Fire is always hot. Example Check whether the following sentences are statements.
Give reasons for your answer. (i) is less than . (ii) Every set is a finite set. (iii) The sun is a star.
(iv) Mathematics is fun. (v) There is no rain without clouds. (vi) How far is Chennai from here? Solution (i) This sentence is false because is greater than .
Hence it is a statement. (ii) This sentence is also false since there are sets which are not finite. Hence it is a statement. (iii) It is a scientifically established fact that sun is a star and, therefore, this sentence is always true.
Hence it is a statement. (iv) This sentence is subjective in the sense that for those who like mathematics, it may be fun but for others it may not be. This means that this