sentence is not always true. Hence it is not a statement. MATHEMATICS (v) It is a scientifically established natural phenomenon that cloud is formed before it rains. Therefore, this sentence is always true.
Hence it is a statement. (vi) This is a question which also contains the word “Here”. Hence it is not a statement. The above examples show that whenever we say that a sentence is a statement we should always say why it is so.
This “why” of it is more important than the answer. EXERCISE . . Which of the following sentences are statements?
Give reasons for your answer. There are days in a month. Mathematics is difficult. (iii) The sum of and is greater than .
(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 (– ) and is .
(viii) The sum of all interior angles of a triangle is °. (ix) Today is a windy day. (x) All real numbers are complex numbers. .
Give three examples of sentences which are not statements. Give reasons for the answers. . New Statements from Old We now look into method for producing new statements from those that we already have.
An English mathematician, “George Boole” discussed these methods in his book “The laws of Thought” in . Here, we shall discuss two techniques. As a first step in our study of statements, we look at an important technique that we may use in order to deepen our understanding of mathematical statements. This technique is to ask not only what it means to say that a given statement is true but also what it would mean to say that the given statement is not true.
. . Negation of a statement The denial of a statement is called the negation of the statement. Let us consider the statement: p: New Delhi is a city The negation of this statement is MATHEMATICAL REASONING It is not the case that New Delhi is a city This