Which of the following sets are functions from the set of first components to the set of second
components?
(a) {(b, a), (d, c), (a, e), (g, f)}
(b) {(a, b), (b, a), (c, c), (a, c)}
(c) {(b, a), (c, a), (b, b), (c, b)}
Elementary math? Really????
MTH 213
To determine if each set is a function from the set of first components to the set of second components, we need to ensure that each first component is mapped to a unique second component.
Let's analyze each set:
(a) {(b, a), (d, c), (a, e), (g, f)}
In this set, each first component (b, d, a, g) is mapped to a unique second component (a, c, e, f). Therefore, this set is a function.
(b) {(a, b), (b, a), (c, c), (a, c)}
In this set, the first component 'a' appears twice, and it is mapped to two different second components (b and c). This violates the uniqueness rule, so this set is NOT a function.
(c) {(b, a), (c, a), (b, b), (c, b)}
In this set, both first components (b and c) are mapped to the same second component 'a'. This violates the uniqueness rule, so this set is NOT a function.
In summary:
(a) is a function.
(b) and (c) are not functions.