PRACTICE PROBLEMS ON OPERATIONS ON SET

(1)  If A⊂B,then show that AUB  =  B (use venn diagram)   Solution

(2)  If A⊂B, then find A∩B and A\B (use venn diagram)   Solution 

(3)  Let P  =  {a, b, c}, Q  =  {g, h, x, y} and R = {a, e, f, s}. Find the following

(i)  P\R    (ii)  Q∩R        (iii)  R\(P∩Q)        Solution

(4) If A = {4, 6, 7, 8, 9}, B = {2, 4, 6} and C = {1, 2, 3,4 , 5, 6},then find

(i) AU(B∩C)    (ii) A∩(BUC)       (iii) A\(C\B)    Solution

(5)  Given A = {a, x, y, r, s}, B = {1, 3, 5, 7, -10},verify the commutative property of set union.   Solution

(6)  Verify the commutative property of set intersection for A = {l, m, n, o, 2, 3, 4, 7} and B = {2, 5, 3, -2, m, n, o, p}   Solution

(7) For A = {x|x is a prime factor of 42}, B ={x|5 < x ≤ 12, x ∈ N} and C = {1, 4, 5, 6} verify AU(BUC)  =  (AUB)UC.   Solution

(8) Given P  =  {a, b, c, d, e} Q  =  {a, e, i, o, u} and R  =  {a, c, e, g}. Verify the associative property of set intersection.    Solution

(9) For A = {5, 10, 15, 20} B = {6, 10, 12, 18, 24} and C = {7, 10, 12, 14, 21, 28} verify whether A\(B\C) = (A\B)\C. Justify your answer.  Solution

(10) Let A = {-5, -3, -2, -1} B = {-2, -1, 0} and C = {-6, -4, -2}. Find A\(B\C) and (A\B)\C. What can we conclude about set difference operation?  Solution

(11) For A = {-3, -1, 0, 4, 6, 8, 10} B = {-1, -2, 3, 4, 5, 6} and C = {-1, 2, 3, 4, 5, 7}, show that

(i) AU(B∩C)  =  (AUB)∩(AUC)

(ii) A∩(BUC)  =  (A∩B)U(A∩C)     Solution

(iii) Verify using venn diagrams

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