If A = {1,3,5,7,9}, B = {1,5,6,7} and C = {1,2,4,6,8,9} find:
i) A U B
That mean to list all numbers that are either in A, in B, or in both.
So A U B = {1,3,5,6,7,9}, for they are in A, B or both.
ii) the complement of (A U B)
That means to list all the numbers that are listed in one of the sets
above but which are NOT in A U B, which we just found in i):
Complement of A U B is {2,4,8}, for these are the ones not in A U B
iii) the intersection of B and C
This means to list ONLY the ones that are in BOTH B and C
Intersection of B and C = {1,6}
iv) find n(A U B)
That means to count the elements in A U B. There are 6.
v) list all the subsets of B
B = {1,5,6,7}
There is just one subset with no members, the empty set,
or
There are four subsets with just one member:
{1}, {5}, {6}, {7}
There are six subsets with two members:
{1,5), (1,6), (1,7}, {5,6}, {5,7}, {6,7}
There are four subsets with three members:
(1,5,6), (1,5,7}, {1,6,7}, {5,6,7}
There is just one subset with four members,
namely the whole set A:
{1,5,6,7}
So altogether there are 1+4+6+4+1 or 16 subsets of {1,5,6,7}.