Chapter 2.5, Problem 16E

Consider the following one-to-one correspondence between the set B of all odd integers and the set N of all natural numbers:

$\begin{array}{l}N=\left\{1,2,3,4,5,\mathrm{...}\right\}\\ \updownarrow \updownarrow \updownarrow \updownarrow \updownarrow \\ B=\left\{1,-1,3,-3,5,\mathrm{...}\right\}\end{array}$

Where an even natural number $n$ corresponds to the negative odd integer $1-n$ and odd number $n$ corresponds to the odd integer $n$.

a. Find the 345th odd integer, that is, find the element of B that corresponds to $345\in N$.

b. Find the clement of N that corresponds to $241\in B$

c. Find the clement of N that corresponds to $-759\in B$

d. Find $n\left(B\right)$