SETS AND FUNCTIONS.

EXERCISE 1.1
(1) If A ⊂ B,then show that A U B = 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) A U (B ∩ C) (ii) A ∩ (B U C)    (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 A U (B U C) = (A U B) U C.   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) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)     Solution
(iii) Verify using venn diagrams