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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. |
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Answer» (i)The negation of the first statement is “the number x is a rational number”. This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number. Therefore, the given statements are negations of each other. (ii) The negation of the first statement is “the number x is not a rational number”. This means that the number x is an irrational number, which is the same as the second statement. Therefore, the given statements are negations of each other. |
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