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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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DM - Grand Test -Q5


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+2 votes

Which of the following is the negation of the statement, “For all odd primes p < q there exists positive non-primes r < s such that p^2 + q^2 = r^2 + s^2."

(a) For all odd primes p < q there exists positive non-primes r < s such that p^2+q^2 \neq r^2 + s^2.

(b) There exists odd primes p < q such that for all positive non-primes r < s, p^2+q^2 =r^2 + s^2.

(c) There exists odd primes p < q such that for all positive non-primes r < s, p^2+q^2 \neq r^2 + s^2.

(d) For all odd primes p < q and for all positive non-primes r < s, p^2 + q^2 \neq r^2 + s^2.

asked Aug 30, 2020 by gbeditor-2 (72,840 points)
reshown Aug 31, 2020 by gbeditor-2

1 Answer

0 votes
 
Best answer

Option C is correct. 

Given : 

“For all odd primes p < q there exists positive non-primes r < s such that p^2 + q^2 = r^2 + s^2."

 

Negation will be : There exists odd primes p < q such that for all positive non-primes r < s, p^2+q^2 \neq r^2 + s^2.

 

NOTE that : \neg \exists x P(x) = \forall x \neg P(x) \newline \neg \forall x P(x) = \exists x \neg P(x)

answered Sep 9, 2020 by deepak-gatebook (226,240 points)
Answer:

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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