CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
Let A = {1, 2, 3, 4} and a relation R from A to A be defined by R = {(x, y): y = x + 1}. How many ordered pairs does R contain, and what is its range?
R has 3 pairs, (1,2), (2,3) and (3,4), with range {2, 3, 4}. The pair (4,5) is not allowed because 5 does not belong to A, so the relation from A to A cannot contain it.
- A3 pairs; range {2, 3, 4}Correct
- B4 pairs; range {2, 3, 4, 5}
- C3 pairs; range {1, 2, 3}
- D4 pairs; range {1, 2, 3, 4}
Explanation
y must lie in A. Pairs are (1,2), (2,3), (3,4); (4,5) is excluded since 5 is not in A. So there are 3 pairs and the range is {2,3,4}. Option 2 wrongly includes 5.
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