1. set [ Show that if F is a function and dom(F) is a set then F is a

Let X-(1, 2, 3, 4, 5, 6). Define the functionf from P(X) to (0, 1] as the power set. What is f((2,5|)? O 020050 O 100100 O 01001 O 010010

Suppose f: R → R is a function from the set of real numbers to the same set with f(x) = x + 1. We write £ to represent fo f and fatl= fof. Is it true that £22o f = fo f?? Why? Is the set {g: R R | gof=fog} infinite? Why?

Prove that f is an identity function of itself.

Let A and B be sets. Let f : A → B be a function. Let S ⊆ A be a subset. Prove that graph(f|S) = graph(f) ∩ (S × B).

Consider the set M = {0, 2, 4, 6} and N = {1, 3, 5, 7}. Determine if each of the following ordered pairs is a function with domain M and codomain N. If you state it is a function, then determine if it is one-to-one and/or onto. a. {(0,2), (2,4), (4,6), (6,0)} b. {(6,3), (2,1), (0,3), (4,5)} c. {(2,3), (4,7), (0,1), (6,5)} d. {(2,1), (4,5), (6,3)} e. {(6,1), (0,3), (4,1), (0,7), (2,5)}

This question confuses me, I dont get what is being asked? How do I approach this? "Let A be a nonempty set and let B be a subset of the power set P(A) of A. Define a relation R from A to B byxRY if x ∈ Y. Give an example of two sets A and B that illustrate this. What is R for these two sets?"