Entity$-$Relationship Model $(12$ points, $4$ points for each$)$

Consider the following entity$-$relationship diagram:

Three$-$way relationships in supplements represent that certain Suppliers supply certain Products for

certain Projects. The relationships also record the quantity for each supplement.

$(1)$ Transform the $3-$way relationship to binary relationships.

$(2)$ Now suppose we add an arrow into the Projects entity set:

Briefly state in English the real$-$world assumption that is encoded when we add this arrow.

$(3)$ Using the standard translation from E$/$R diagrams to relations, specify the relation for the Supply

relationship set. Assuming the constraint added in part $(2),$ also specify a key for the relation.