Chapter 8.4, Problem 4MC

If S is the set of students in Ms. Carmel’s class, and A is any subset of S, we define: $f\left(A\right)=\bar{A}$ (where $\bar{A}$ is the complement of $A$). Notice that the input in this function is a subset of S and the output is a subset of S. Answer the following.

a. Explain why $f$ is a function and describe the domain and the range of $f$.

b. If there are $20$ children in the class, what are the number of elements in the domain and the number in the range? Explain.

c. Is the function in this question a one-to-one correspondence? Justify your answer.