$5\mathrm{.}2\mathrm{.}3$: Using the bijection rule to count binary strings with even parity.

help$\_$outline

Let B$=\{0,1\}.$ Bn is the set of binary strings with n bits. Define the set En to be the set of binary strings with n bits that have an even number of $1\text{'}$s$.$ Note that zero is an even number, so a string with zero $1\text{'}$s $($i$.$e$.,$ a string that is all $0\text{'}$s$)$ has an even number of $1\text{'}$s$.$

$($a$)$

Show a bijection between B$9$ and E$10.$ Explain why your function is a bijection.

$($b$)$

What is $|$E$10|?$