Question

Which of the following relations are functions? Choose all that apply. Assume that each different variable has a different value.

a) {(a, b), (b, a), (c, c), (e, d)}
b) {(1, 4), (c, d), (0, 6)}
c) {(6, b), (c, d), (2, c), (4, a)}
d) {(a, b), (5, c), (c, d), (d, )}

Answer 1

A function is a special type of relation where each element in the domain is paired with exactly one element in the range. To determine if a relation is a function, we need to check if each element in the domain appears only once in the relation. The relations (b) and (c) are functions.

Step-by-step explanation:

A relation is a set of ordered pairs, where each element in the domain is paired with exactly one element in the range. A function is a special type of relation where each element in the domain is paired with exactly one element in the range. To determine if a relation is a function, we need to check if each element in the domain appears only once in the relation.

Looking at the given options:

1. {(a, b), (b, a), (c, c), (e, d)} - Not a function because both a and b appear twice in the relation.
2. {(1, 4), (c, d), (0, 6)} - A function because each element in the domain appears only once in the relation.
3. {(6, b), (c, d), (2, c), (4, a)} - A function because each element in the domain appears only once in the relation.
4. {(a, b), (5, c), (c, d), (d, )} - Not a function because a appears twice in the relation.

Therefore, the relations (b) and (c) are functions.