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Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...

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

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