Are the following relations on P({0, 1, 2, 3}) equivalence relations? If so, list the equivalence classes under the relation; if not, explain why not.
1 (A, Bi) ∈ R1 if and only if (i) A and B are nonempty and the largest element in A equals the largest
element in B, or (ii) if A = B = ∅.
2 (A, Bi
)∈ R2 if and only if the sum of the elements in A equals the sum of the elements in B.
3 (A, Bi) ∈ R3 if and only if the sum of the elements in A equals the sum of the elements in B and the
largest element in A equals the largest element in B. (That is, R3 = R1 ∩ R2.)
4 (A, Bi
∈ R4 if and only A ∩ B 6= ∅.
5 (A, Bi) ∈ R5 if and only |A| = |B|.