Let S be the set of all strings of a's and b's of length 4. Let B = {0, 1} %3! Let f:S → B be defined as follows: 1 if s has an a in the rightmost place f(s)- 0 if s does not have an a in the rightmost place Evaluate the following: a) f(aaaa) b) f(abbb) c) f(abab) d) f(bbba) e)List all of the ordered pairs for which f(s) = 1.

7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.

Let S: Z+Z+ be a function given by the following:S(n) S(1) = S(6) = S(29) = Preview Preview Preview = sum of the divisors of n, for all n E€ Z+. Find the following.

(6a)  how many different functions f : A → B can be defined if m=3 and n=5?  (6b) if m=4 and n=6 then how many different one-to-one functions f : A →B can be defined? (6c) if m=5 and n=4 then how many different onto functions f : A → B can be defined?