Menu

1. Decide, among the following sets, which sets are subsets of one and another:

A={x : x∈R and x satisfy x^{2}–8x+12=0}, B={2,4,6}, C={2,4,6,8, . . . }, D={6}.

(iii) If A⊂B and B⊂C, then A⊂C

3. Let A, B, and C be the sets such that A∪B=A∪C and A∩B=A∩C. Show that B=C.

4. Show that the following four conditions are equivalent:

5. Show that if AB, then C–B ⊂ C–A.

6. Show that for any sets A and B,

A=(A∩B)∪(A–B) and A∪(B–A)=(A∪B).

7. Using properties of sets, show that

8. Show that A∩B=A∩C need not imply B=C.

9. Let A and B be sets. If A∩X=B∩X=\(\phi\) and A∪X=B∪X for some set X, show that A=B.

(Hints A=A∩(A∪X), B=B∩(B∪X) and use Distributive law)

10. Find sets A, B and C such that A∩B, B∩C and A∩C are non-empty sets and A∩B∩C=\(\phi\).