Category: Sets

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).

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.

8. Show that A∩B=A∩C need not imply B=C. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1.

7. Using properties of sets, show that (i) A∪(A∩B)=A         (ii) A∩(A∪B)=A. Sets Miscellaneous Exercise Previous Next Class

6. Show that for any sets A and B, A=(A∩B)∪(A–B) and A∪(B–A)=(A∪B). Sets Miscellaneous Exercise Previous Next Class

5. Show that if AB, then C–B ⊂ C–A. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise

4. Show that the following four conditions are equivalent: (i) A⊂B               

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

2. In each of the following, determine whether the statement is true or false. If it is true,

1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and