Category class 11

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) Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets,…

8. Show that A∩B=A∩C need not imply B=C. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x satisfy x2–8x+12=0}, B={2,4,6}, C={2,4,6,8,…

7. Using properties of sets, show that (i) A∪(A∩B)=A         (ii) A∩(A∪B)=A. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x…

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

5. Show that if AB, then C–B ⊂ C–A. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x satisfy x2–8x+12=0}, B={2,4,6},…

4. Show that the following four conditions are equivalent: (i) A⊂B                 (ii) A–B=(phi)             (iii) A∪B=B             (iv) A∩B=A Sets Miscellaneous Exercise Previous Next Class…

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 Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another:…

2. In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x∈A and A∈B, then x∈B (ii) If A⊂B and B∈C, then…

1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x satisfy x2–8x+12=0}, B={2,4,6}, C={2,4,6,8, . . . }, D={6}. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among…