Let F be the function defined in exercise 4b of Section 51 I

Let F be the function defined in exercise 4(b) of Section 5.1. In exercise4 of Section 5.2, you showed that F is one-to one and onto, so F1 :B B. If X B, what is F1(X)?

exercise 4(b) of Section 5.1

4. (b) Let A = {1, 2, 3} and B = P (A). Let F : B B be the function defined by the formula F(X) = A \\ X. What is F({1, 3})?

exercise4 of Section 5.2

4. Which of the functions in exercise 4 of Section 5.1 are one-to-one? Which are onto?

Solution

4b.

F({1,3})=A\\{1,3}={2}

4.

Let, F(X)=F(Y)

Hence,

A\\X=A\\Y

But X and Y are subsets of A

So A\\X =A\\Y ie the elements in A but not in X and in A but not in Y are the same.

Hence elements in X and A , elements in Y and A are the same but X,Y are subsets of A

Hence, X=Y

Hence, F is one to one.

For any set ,X, in B

F(A\\X)=(A\\(A\\X))=X

Hence, F is onto