Question

Let A = {0, 1, 2, 3, 4}. If R is a relation defined on A such that R= {(x, y): $x \epsilon A$, $y \epsilon A$, min{x, y} = 2}. Then, the number of elements in R is

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Answer 1

5

Answer 2

The relation R is defined as pairs (x, y) from A such that min{x, y} = 2. This implies that either x=2 and y≥2, or y=2 and x≥2.

1. If x=2, then y can be {2, 3, 4} (from A), giving pairs (2,2), (2,3), (2,4).
2. If y=2, then x can be {2, 3, 4} (from A), giving pairs (2,2), (3,2), (4,2).

Combining these and removing duplicates, R = {(2,2), (2,3), (2,4), (3,2), (4,2)}. The number of elements in R is 5.