Determine the validity of each argument by converting the premises and the conclusion to symbolic form and applying the rules of inference. If the argument is valid, state the rule of inference that was used. If the argument is invalid, state the type of error.

$($i$)$ Symbolic form

$($ii$)$ Valid or not

$($iii$)$ Rule of inference $($if valid$)$ OR type of error $($if invalid$)$

a$.$ If Jared gets a year$-$end bonus, then he will book a cruise for his family. Jared does not get a year$-$end bonus.

Therefore, Jared does not book a cruise for his family.

b$.$ If aliens exist, then they are smarter than humans. If aliens are smarter than humans, then they will conquer Earth. Therefore, if aliens exist, then they will conquer Earth.