Let D be the set of all finite subsets of positive integers. Define a function T:Z* → D as follows: For each positive integer n, T (n) = the set of positive divisors of n. Find the following: a. T(1) d. T(5) с. Т(17) f. T (21) b. Т (15) e. T(18)

Let S = {0,1}. Exhibit all functions S → S and classify them as injective, surjective, bijective, or none.

Let f:Z>Z be a function given by f(x) = -3x + 1. Recall that Z = the set of all integers, that is, Z = {.,-2,-1, 0, 1, 2,...

[D] Consider the function F: {1,5, 8} × {6, 10} → {0, 1, 2, 3, 4, 5} defined as follows: F: (a, b) → (4a + b)mod 6 (D.1) Fill in the ordered pairs in the diagram below to indicate the elements in the domain of F. Then draw in arrows to complete the diagram so that it correspondes to the function. ( • 0 • 1 • 2 • 3 • 4 • 5 (D.2) What is the range of F? (D.3) What is the co-domain of F? 3/5 (D.4) What is the preimage (inverse image) of 3? (D.5) What is the preimage (inverse image) of 0? (D.6) Is F one-to-one? If not provide a counterexample. (D.7) Is F onto? If not provide a counterexample.

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