NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 4
Total: 25
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.
(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.
Solution:
(i) Let p : The number x is not a rational number.
q : The number x is not an irrational number.
Now, ~p : The number x is a rational number.
~q : The number x is an irrational number.
∴ ~p = q and ~q = p
Thus, p and q are negations of each other.
(ii) Let p : The number x is a rational number.
q : The number x is an irrational number.
Now, ~p: The number x is not a rational number.
~q: The number x is not an irrational number.
∴ ~p = q and ~q = p
Thus, p and q are negations of each other.
q : The number x is not an irrational number.
Now, ~p : The number x is a rational number.
~q : The number x is an irrational number.
∴ ~p = q and ~q = p
Thus, p and q are negations of each other.
(ii) Let p : The number x is a rational number.
q : The number x is an irrational number.
Now, ~p: The number x is not a rational number.
~q: The number x is not an irrational number.
∴ ~p = q and ~q = p
Thus, p and q are negations of each other.
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