Megan has recently been training to join the Eagles as a kicker. In order to do so$,$ she sets up

three goals and calls them names of fellow TA$$s that always steal her boba, Sam, Thomas, and

Richard, in order to motivate herself to kick footballs into the goals. While kicking footballs

into the named goals, Megan hypothesizes sets S$,$ T$,$ and R $($in honor of Sam, Thomas, and

Richard$),$ and wants to see what statements she can prove about these sets. Help Megan prove

or disprove the following properties about the sets. Megan demands that you look at $2.$sp$2$ to

help solve this problem. Any solution that uses Venn Diagrams is not rigorous and will receive

no credit.

$($a$)$ S $\backslash ($T $\backslash$ R$)=($S $\backslash$ T $)\backslash$ R

$($b$)$ S $\backslash ($T $\backslash$ R$)($S $\backslash$ T $)\backslash$cup R$.$

$($c$)$ S $\backslash$ R $=($S $\backslash ($T $\backslash$cup R$))\backslash$cup $(($S $\backslash$cap T $)\backslash$ R$)$

$($d$)$ if $$ y such that y in S $\backslash$times T $$ y in T $\backslash$times S$,$ x such that x in S $$ x in T $.$