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Let S = {1, 2, 3, 4, 5}. If R = {(x, y): x + y < 6}, then how many ordered pairs are in R?

1. 8
2. 10
3. 6
4. 5

Correct answer: 10

Solution

For x+y<6 with x,y in {1..5}: x=1 gives y=1..4 (4), x=2 gives y=1..3 (3), x=3 gives y=1,2 (2), x=4 gives y=1 (1), x=5 gives none. Total = 4+3+2+1 = 10.

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