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Question

Check whether the following pair of statements are negations of each other. Give reasons for your answer.

(i) x +y =y +x is true for every real numbers x and y.

(ii) There exists real numbers x and y for which x + y = y + x.

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Solution

Let p : x + y = y + x is true for every real numbers x and y.
q: There exists real numbers x and y for which x + y = y + x.

Now ~p: There exists real numbers x and y for which x+yy+x. Thus ~pq.


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