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Questions › JNU › JNU SSS 2011 › Q42
1 mark, −0.25Mathematics › Logic and proof techniques › Quantifiers and their negationModerateabout 1 min

JNU SSS 2011 Question 42: Logic and proof techniques

Let P(n,m)P(n, m)P(n,m) be a property about two integers nnn and mmm. If we want to disprove the claim that 'for every integer nnn, there exists an integer mmm such that P(n,m)P(n, m)P(n,m) is true', then we need to prove that

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Let P(n, m) be a property about two integers n and m. If we want to disprove the claim that 'for every integer n, there exists an integer m such that P(n, m) is true', then we need to prove that (A) there exist integers n, m such that P(n, m) is false (B) there exists an integer m such that P(n, m) is false for all integers n (C) there exists an integer n such that P(n, m) is false for all integers m (D) for every integer n, there exists an integer m such that P(n, m) is false

Logic and proof techniques has come up 73 times in 3 exams since 2004.

What this question tests

This question is on Quantifiers and their negation, part of Logic and proof techniques in Mathematics.

Statements with 'for all' and 'there exists', and how they change when negated or reordered.

TestStop has 6 past-paper questions on this subtopic.

Practise Logic and proof techniquesMore on Quantifiers and their negation

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Question from the JNU SSS 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.