1. Determine whether or not each of the following relations is a function with domain {1, 2, 3, 4}. For any relation that is not a function, explain why it isn’t.
a) f = {(1, 2), (2, 3), (4, 2)}
b) f = {(1, 1), (1, 2), (1, 3), (1, 4)}
c) f = {(1, 4), (2, 3), (3, 2), (4, 1)}
2. Suppose A is the set of students registered at the University of Calgary, and C is the set of courses currently being offered at the University of Calgary. Under what conditions is each of the following a function?
a) {(a, c) | a’s first class each week is in c}
b) {(a, c) | a has a class in c Saturday evening}
3. Let A = {1, 2, 3, 4}. Find the inverse of the following function f: A → A.
a) f = {(1, 2), (2, 4), (3, 3), (4, 1)}
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