QUESTIONS

1. Explain the following with the aid of a Venn diagram.

(a) If A Bc = . (b) If Ac \ Bc then

is equal to; (c) If A = .

(d) If A and B are sets and A B = A B, then (e) If A,B

and C are sets and A \ (B C).

2. Given the sample space = {a,b,c}. Construct the following;

(a) Power set (2).

(b) a ring from the power set (2).

(c) a - ring form the power set (2).

(d) an algebra form the power set (2).

(e) an - algebra form the power set (2).

3. Let X = {1,2}, show that

(a) S = {,{1}}

(b) S = {,{1},X}

Is S a ring or algebra.

4. Let X = {0,1,2,3} and let

= {,X,{0,1},{0,2},{0,3},{2,3},{1,3},{1,2}}

Is an algebra?

5. Given R = (-,+) and X R. Construct a - algebra for;

(a) X = (0,1]

(b) X = {(0,2],(3,4]}