This statement is true because we know that square is a quadrilateral such that its four sides are equal. (iii) The negation of the statement is It is false that every natural number is greater than . This can be rewritten as There exists a natural number which is not greater than . This is a false statement.
(iv) The negation is It is false that the sum of and is . This can be written as The sum of and is not equal to . This statement is true. .
. Compound statements Many mathematical statements are obtained by combining one or more statements using some connecting words like “and”, “or”, etc. Consider the following statement p: There is something wrong with the bulb or with the wiring. This statement tells us that there is something wrong with the bulb or there is MATHEMATICAL REASONING something wrong with the wiring.
That means the given statement is actually made up of two smaller statements: q: There is something wrong with the bulb. r: There is something wrong with the wiring. connected by “or” Now, suppose two statements are given as below: p: is an odd number. q: is a prime number.
These two statements can be combined with “and” r: is both odd and prime number. This is a compound statement. This leads us to the following definition: Definition A Compound Statement is a statement which is made up of two or more statements. In this case, each statement is called a component statement.
Let us consider some examples. Example Find the component statements of the following compound statements. The sky is blue and the grass is green. It is raining and it is cold.
(iii) All rational numbers are real and all real numbers are complex. (iv) is a positive number or a negative number. Solution Let us consider one by one (i) The component statements are p: The sky is blue. q: The grass is green.
The connecting word is ‘and’. (ii) The component statements are p: It