that compound statements are actually made-up of two or more statements connected by the words like “and”, “or”, etc. These words have special meaning in mathematics. We shall discuss this mattter in the following section. EXERCISE .
. Write the negation of the following statements: Chennai is the capital of Tamil Nadu. is not a complex number (iii) All triangles are not equilateral triangle. (iv) The number is greater than .
(v) Every natural number is an integer. . Are the following pairs of statements negations of each other: The number x is not a rational number. The number x is not an irrational number.
The number x is a rational number. The number x is an irrational number. . Find the component statements of the following compound statements and check whether they are true or false.
Number is prime or it is odd. All integers are positive or negative. (iii) is divisible by , and . .
Special Words/Phrases Some of the connecting words which are found in compound statements like “And”, MATHEMATICS “Or”, etc. are often used in Mathematical Statements. These are called connectives. When we use these compound statements, it is necessary to understand the role of these words.
We discuss this below. . . The word “And” Let us look at a compound statement with “And”.
p: A point occupies a position and its location can be determined. The statement can be broken into two component statements as q: A point occupies a position. r: Its location can be determined. Here, we observe that both statements are true.
Let us look at another statement. p: is divisible by , and . This statement has following component statements q: is divisible by . r: is divisible by .
s: is divisible by . Here, we know that the first is false while the other two are true. We have the following rules regarding the connective “And” . The compound statement with ‘And’ is true if all its component statements are true.
. The component statement with