Answer
a. True.
b. False.
c. True.
d. False.
Work Step by Step
The definition of a function is used in each part. A function f: X → Y satisfies 2 properties:
1. Every element in X is related to an element in Y.
2. No single x∈X is related to more than one y∈Y.
a. By the second property, since each element in X relates to only 1 element in Y then if both elements are the same in X then they must relate to the same element in Y.
b. The properties of a function do not stop 2 different elements in X from relating to the same element in Y. That is, 2 different elements e.g. a, b ∈ X can point to the same y∈Y. So if 2 elements in Y are the same it does not guarantee that the elements in X that are related to those 2 elements in Y are equal as well.
c. This is true for the same reason that the previous question (b) is false. The properties of a function do not prohibit 2 different elements in X from pointing to the same element in Y.
d. This is false because it violates property (2) which is that no element in X can point to more than one element in Y.
**Note relate and point mean the same thing in this context.