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Question
Are the followingpairs of statements negations of each other?
(i) The number xisnot a rational number.
The number xis not an irrational number.
(ii) The numberx isa rational number.
The number xis an irrational number.
Are the followingpairs of statements negations of each other?
(i) The number xisnot a rational number.
The number xis not an irrational number.
(ii) The numberx isa rational number.
The number xis an irrational number.
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Solution
(i) Thenegation of the first statement is “the number xis a rational number”.
Thisis same as the second statement. This is because if a number is notan irrational number, then it is a rational number.
Therefore,the given statements are negations of each other.
(ii) The negation ofthe first statement is “the number xis not a rational number”. This means that the number xis an irrational number, which is the same as the second statement.
Therefore,the given statements are negations of each other.
(i) Thenegation of the first statement is “the number xis a rational number”.
Thisis same as the second statement. This is because if a number is notan irrational number, then it is a rational number.
Therefore,the given statements are negations of each other.
(ii) The negation ofthe first statement is “the number xis not a rational number”. This means that the number xis an irrational number, which is the same as the second statement.
Therefore,the given statements are negations of each other.
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