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in Mathematics by (54.8k points)

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

1 Answer

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(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 a rational number (∵ when a number is not irrational, it is a rational) 

~p = q and ~q = p 

⇒ given pairs of statements 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 an irrational number (∵ When a number is not rational, it is irrational) 

∴ ~p = q and ~q = p 

⇒The pairs are negations of each other.

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