Final answer:
To determine which relations on the set {a, b, c, d} are equivalence relations and contain (a, b) and (b, d), one example is {(a, b), (b, d), (d, a)} as it is reflexive, symmetric, and transitive.
Step-by-step explanation:
An equivalence relation on a set is a relation that is reflexive, symmetric, and transitive.
To determine which relations on the set {a, b, c, d} are equivalence relations and contain (a, b) and (b, d), we need to check if these relations satisfy these three properties.
One example of such a relation is {(a, b), (b, d), (d, a)} as it is reflexive, symmetric, and transitive.