$9\mathrm{.}47$ Consider the following $3$NF relations about a sorority or fraternity:

MEMBER$($Member$\_$ID$,$Name,Address,Dues$\_$Owed$)$

OFFICE$($Office$\_$Name,Officer$\_$ID$,$Term$\_$Start$\_$Date,$\_$Budget$)$

EXPENSE$($Ledger$\_$Number,Office$\_$Name,ExpeAse$\_$Date,$\_$Amt$\_$Owed$)$

PAYMENT$($Check$\_$Number,Expense$\_$Ledger$\_$Number,Amt$\_$Paid$)$

RECEIPT$($Member$\_$ID$,$Receipt$\_$Date,Dues$\_$Received$)$

COMMITTEE$($Committee$\_$ID$,$Officer$\_$in$\_$Charge$)$

WORKERS$($Committee$\_$ID$,$Member$\_$ID$)$

a$.$ Foreign keys are not indicated in these relations. Decide which attributes are foreign keys and justify your decisions.

b$.$ Draw an E$-$R diagram for these relations, using your answer to Problem and Exercise $9\mathrm{.}47$a$.$

c$.$ Explain the assumptions you made about cardinalities in your answer to Problem and Exercise $9\mathrm{.}47$b$.$ Explain why it is said that the E$-$R data model is more expressive or more semantically rich than the relational data model.