Q.If U = {x/x∈N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8 9, 12}. Write down the set A-B.

The difference of A and B, written A−B (also expressible as A∩B'), is the set of elements in A but NOT in B: A−B = {x / x∈A, x∉B}. Note B−A is generally a completely different set (in A−B, elements exclusive to A are kept; in B−A, elements exclusive to B are kept) — set difference is NOT commutative, unlike union or intersection. Both A−B ⊆ A and B−A ⊆ B always hold. A useful structural fact: for any two sets, the three pieces A−B, A∩B, and B−A are mutually disjoint (no element belongs to more than one of them), and together they exactly make up A∪B: A∪B = (A−B)∪(A∩B)∪(B−A). This partition — 'only in A', 'in both', 'only in B' — is the natural way to think about any two-set Venn diagram. The SYMMETRIC DIFFERENCE of A and B, written A∆B, is (A−B)∪(B−A) — everything in exactly one of the t …