Consider the following scenario and complete the tasks below:

Memorina Bytesworth is a single$-$honours Computer Science student at Numberland University where she is currently enrolled on four modules of her Level $4$ studies. Each of those modules is worth $30$ credits. Her performance on Level $4$ assessments will be deemed satisfactory $($code name: SATIS$)$ if she passes at least $90$ credits. The SATIS code allows her to progress to Level $5$ of her degree programme and retrieve the failed credits in the following year $($i$.$e$.,$ repeat and pass the failed Level $4$ credits whilst on Level $5$ studies$).$ However, she is allowed to resit any of the failed modules during the summer vacation $($code name: VAC$)$ if she has a minimum of $60$ credits, otherwise she will be required to repeat the Level $4$ year in full $($code name: RPT$).($i$)$ Produce a truth table that summarises all possible combinations of Memorina$$s potential progression outcomes.

$($ii$)$ Formulate a Boolean expression that represents the truth table in $($i$)$ above.