1
Question
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.
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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Solution
(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.
(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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