Question 2 Are the following pairs of statements negations of each other?
(i) The number x is not a rational number.
The number x is not an irrational number.
(ii) The number x is a rational number.
The number x is an irrational number.
Class X1 - Maths -Mathematical Reasoning Page 329
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negation : if word ' not ' is not given in the statement , then insert word 'not ' in the statement . if word 'not ' given in the statement then, remove word 'not' from the statement .
(i) Negation of the statement, ' the number 'x' is a rational number . now, second statement, ' The number 'x' is not an irrational number or we can say that the number 'x' is a rational .Hence, both statements are Negations of each other .
(ii) Negation of the statement, ' The number 'x' is not a rational number or we can say that the number 'x' is an irrational number . The second statement is same . Therefore both are Negations of each other .
(i) Negation of the statement, ' the number 'x' is a rational number . now, second statement, ' The number 'x' is not an irrational number or we can say that the number 'x' is a rational .Hence, both statements are Negations of each other .
(ii) Negation of the statement, ' The number 'x' is not a rational number or we can say that the number 'x' is an irrational number . The second statement is same . Therefore both are Negations of each other .
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