Let R$($A$,$B$,$C$)$ and S$($A$,$B$,$C$)$ be two relations, and no attributes can have null value. Determine whether each of the following equations always holds in which R$,$ S$,$ and all operations are interpreted to be sets and set$-$operations.

What if R$,$ S$,$ and all operations are bags and bag$-$operations? Please explain your answer in detail.

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a$).($R INTERSECT S$)=($R JOIN S$)$

b$).((($R $-$ S$)$ UNION $($S $-$ R$))$ INTERSECT $($R INTERSECT S$))=$ EMPTYSET

c$).$ DELTA$($R$)=$ GAMMA$\_\{$A$,$B$,$C$\}($R$)$

d$).($R UNION S$)=$ R