Chapter 8.CR, Problem 21CR

To determine

(a)

The correspondences “$A$ is the set of college students, and $B$ is the set of majors. To each college student corresponds his or her major” from $A$ to $B$ describe a function or not and find its range.

To determine

(b)

The correspondences “$A$ is the set of books in the library, and $B$ is the set $N$ of natural numbers. To each book corresponds the number of pages in the book” from $A$ to $B$ describe a function or not and find its range.

To determine

(c)

The correspondences “$A=\left\{\left(a,b\right)|a\in N\text{and}b\in N\right\},\text{and}B=N$ To each element of $A$ corresponds the number $4a+2b$” from $A$ to $B$ describe a function or not and find its range.

To determine

(d)

The correspondences “$A=N\text{and}B=N$ If $x$ is even, then $f\left(x\right)=0$, and if $x$ is odd, then $f\left(x\right)=1$” from $A$ to $B$ describe a function or not and find its range.

To determine

(e)

The correspondences “$A=N\text{and}B=N$. To each natural number corresponds the sum of its digits” from $A$ to $B$ describe a function or not and find its range.