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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

A relation R is defined from A = {1, 2, 3, 4, 5} to B = {1, 2, 3, 4, 5} by R = {(x, y): y = x + 2}. How many ordered pairs does R contain, and what is the range of R?

R contains the pairs (1,3), (2,4) and (3,5), because x = 4 and 5 give y = 6 and 7, which are outside B. So R has 3 ordered pairs and its range is {3, 4, 5}.

  1. A3 pairs; range {3, 4, 5}Correct
  2. B5 pairs; range {3, 4, 5, 6, 7}
  3. C3 pairs; range {1, 2, 3}
  4. D4 pairs; range {2, 3, 4, 5}

Explanation

Pairs with y in B: (1,3), (2,4), (3,5). For x = 4 or 5, y = 6 or 7, which are not in B. So R has 3 pairs and the range is {3, 4, 5}. Listing {1, 2, 3} confuses domain with range.

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