3. Let A = [0,1) = {x: 0 <= x<1} and B = [-1/2, 1/2] = {x: -1/2 <= x <= 1/2}

Identify the following sets:

(i) AUB

(ii) AnB

(iii) A'

(iv) B'

Find (AUB)' and show this set is A' n B'. Prove generally that (AUB)' = A' n B'

EXTENSION

The symmetric difference between two sets is defined as

A (small triangle, can't type it) B = (A - B) U (B-A)

(a) Draw Venn Diagrams to show that this is equivalent to (AUB) - (AnB)

(b) Prove (algebraically) that (A-B) U (B-A) = (AUB) -(AnB)

(c)If A is the set of even integers and B the set of integers which are multiples of 3, describe the set (AUB) - (AnB)