Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › JNU › JNU SSS 2010 › Q70
1 mark, −0.5Mathematics › Logic and proof techniques › Quantifiers and their negationModerateabout 2 min

JNU SSS 2010 Question 70: 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 prove 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 should do the following

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Let P(n, m) be a property about two integers n and m. If we want to prove that "for every integer n, there exists an integer m such that P(n, m) is true", then we should do the following (A) Let n and m be arbitrary integers. Then show that P(n, m) is true (B) Find an integer m such that P(n, m) is true for every integer n (C) Let n be an arbitrary integer. Then find an integer m possibly depending on n such that P(n, m) is true (D) Find an integer n and an integer m such that P(n, m) is true

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

Similar questions from other papers

  • CUET-PG 2023 Shift 2 · Q100Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If a proposition P implies proposition Q, then we can…
  • JNU SSS 2018 · Q20A student studying the weather for x days observed that (i) it rained on 7 days, morning or afternoon; (ii) when it rained in the afternoon, it was clear in the…
  • JNU SSS 2015 · Q36Which of the following is a possible sequence of combinations for the salesman to visit in two successive years?
  • JNU SSS 2014 · Q32Which of the following is true?
  • JNU SIS 2013 · Q23"All those who have a good voice are good singers." This statement logically implies

Question from the JNU SSS 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.