(1)Let A = {1,2,3,4,5,6}. In each of the following, give an example of a function f : A A with the indicated properties, or explain why no such function exists.

(a)f is bijective, but is not the identity function f(x) = x.

(b)f is neither one-to-one nor onto.

(c)f is one-to-one, but not onto.

(d)(d) f is onto, but not one-to-one.

(2)In each of the following, give an example of a function f : Z Z with the indicated properties, or explain why no such function exists.

(a)f is bijective, but is not the identity function f(x) = x.

(b)f is neither surjective nor injective.

(c)f is surjective, but not injective. (d) f is injective, but not surjective.

(3)Write each of the following as a single logarithm.

(a)log(1) + log(2) + log(3) + log(4) + log(5)