Assume $f$:$AB$ is total function, and A is finite. Replace the $***$ with one of $,,=$ to produce the strongest correct version of the following statements:

$($a$)|f(A)|***|B|.$

$($b$)$ If $f$ is a surjection, then $|A|***|B|.$

$($c$)$ If $f$ is a surjection, then $|f(A)|***|B|.$

$($d$)$ If $f$ is an injection, then $|f(A)|***|A|.$

$($e$)$ If $f$ is a bijection, then $|A|***|B|.$

Write down the reason for your answer.