LAST TIME REVISION SET THEORY (3)

1) List the set A ∪ B, A ∩B, A ∩(B ∪C). Given that,
A={p, q, r,s}, B={q,r,s,t}, C={q,r,t}

2) If P={a,b,c,d,e} and  Q={a,e,i,o,u}, prove that P ⊂ P∪Q and P ∩ Q⊂ P.

3) If A={2,3,4,5} and B={1,2,3,4} show that B - A ≠ A - B.

4) Let S={1,2,3,4,5} be the universal set and let A={3,4,5} and B={1,4,5} be two of its subsets . Verify (A∪B)' = A' ∩B' (dash denotes complement).

5) If A={1,2,3,4}, B={2,3,4,5}, C={1,3,4,5,6,7}, find 
a) A - B
b) A - C
and hence verify that, A - (B ∩C)= (A - B)∪ (A - C).

6) If P={a,b,c,d,e,f} and Q={a,c,e,f}, prove that
(P - Q) ∪ (P∩ Q) = P.

7) If A={x:x is an integer and 1≤ x ≤ 10} and B={x:x is a multiple of 3 and 5≤ x≤ 30} ; find
a) A∪ B
b) A ∩ B
c) A - B
d) B - A

8) Let U={1,2,3,4,5,6,7,8, 9,10} be the universal set. Suppose , A={1,2,3, 4, 5, 6} and B={5,6,7} are its two subsers. Write down the element of A - B and A∩B' (remember B' is the complement of B).

9) If X={x: x is an integer and 6< x ≤20} and Y= {x: x is a multiple of 3 and 0 ≤ x≤ 25}, find 
a) X ∪ Y
b) X∩ Y
c) Y - X
d) X - Y

10) Let S={1,2,3,4,5,6} be the universal set. Let A ∪B= {2,3,4}; Find A'∩B' where A', B' are complement of A and B respectively. Also show that A ∪B and A' ∩ B' are disjoint sets.

11) P={p,q,r,s,t,u} and Q ∩ R={q,r,v,w} ; find
a) (P ∪Q) ∩ (P∪R)
b) (P - Q)∪ (P - R)

12) If A, B, C be three subsets of the universal set S where S={1,2,3, 4,5, 6,7}, A={1, 3, 5, 6} and B∩C ={1,2,6}, find 
a) (A ∪B)∩(A∪ C)
b) B'∪ C'.

13) If U={a,b,c,d,e,f} be the universal set and A, B, C are three subsets of U, where A={a,c,d} and B∪C ={a,d,c,f} , find
a) (A ∩B)∪ (A  ∩ C)
b) (B' ∩ C')

14) Given , A={x: 0< x ≤ 2} and B={x: 1< x<3}; find 
a) A ∩ B
b) A ∪B
c) A - B

15) Let A={}x: 2≤ x <5} and B={x: 3 < x <7} be two subsets of the universal set, S={x:0 < x ≤ 10} ; verify that  (A ∪ B)' = A' ∩B'

16) Given, X∪ Y ={1,2,3,4}, X  ∪ Z={2,3,4,5}, X∩Y={2,3} and X∩Z={2,4}; find X, Y and Z.

17) If aN={ax: x ∈N}, describe 3N ∩ 7N where N is the set of natural numbers.

 

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