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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Let A = {1, 2, 3, 4} and R = {(a, b) : a < b} be a relation on A. How many ordered pairs does R contain, and what is R's nature?

R has 6 pairs and is transitive but neither reflexive nor symmetric. The pairs with a smaller first element are six in number. No pair has equal entries, (2,1) is missing for (1,2), and a<b<c always implies a<c.

  1. A6 pairs; transitive but neither reflexive nor symmetricCorrect
  2. B6 pairs; reflexive and transitive
  3. C10 pairs; transitive and symmetric
  4. D4 pairs; symmetric but not transitive

Explanation

Pairs with a<b: (1,2),(1,3),(1,4),(2,3),(2,4),(3,4), which is 6 pairs. No (a,a) is present, so R is not reflexive. (1,2) is in R but (2,1) is not, so R is not symmetric. If a<b and b<c then a<c, so R is transitive.

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