Write the following relations as sets of ordered pairs and find which of them are functions: {(x, y): x + y = 3, x, y ∈ {0, 1, 2, 3}}

Answer:

If x = 0,

0 + y = 3

y = 3

If x = 1,

1 + y = 3

y = 2

If x = 2,

2 + y = 3

y = 1

If x = 3,

3 + y = 3

y = 0

∴ R = {(0, 3), (1, 2), (2, 1), (3, 0)}

Hence, R is a function.