Example
If U = {3, 6, 7, 12, 17, 35, 36 }, A = {odd numbers }, B = {Numbers divisible by 7 }, C = {prime numbers > 3 } List the elements of
1) A¢ and B¢
2) The subset of C
3) The power set of C
Solution :
1) A = { 3, 7, 17, 35 } Þ A¢ = { 6, 12, 36 }
B = {7, 35 } Þ B¢ = {3, 6, 12, 17, 36 }
2) C = {7,17 } Þ Subset of C = {7}, {17}, {7,17}, f
3) The power set C = the set of all subsets of C = {{7}, {17}, {7,17}, f}
Example
If A = { 2, 4, 6, 8, 10, 12 }, B = {4, 8, 12 }.
1) A  B
2) B  A
3) How many subsets can be formed from the set A ?
4) How many proper subsets can be formed from B ?
Solution :
1) A  B = { 2, 6, 10 }
2) B  A = { }
3) The set A contains 6 elements Þ The number of subsets = 2^{6} = 64
4) n (B) = 3 Þ 2^{3} = 8
\ The number of proper subsets = 23  1 = 8  1 = 7
Example
If U = {
}
1) List the elements of the following sets.
a) A = { x  1 £ x < 4 }
b) B = { x  x < 0 and x = n/2 }, n ÎI
2) Are sets A and B disjoint ? Give reason.
Solution :
1) (a) A = { 3/2, 4/3, 2, 1, 0, }
(b) B = { 3/2, 3, 4 }
2) Yes, negative numbers, which are multiples of 1/2 Ï A
Example
A = { 1, 121, 12321, 1234321 }
B = { 1111^{2} , 111^{2}, 11^{2}, 1^{2} }
State whether A Ì B or B Ì A or A = B
Solution :
Now B = {1111^{2} = 1234321, 111^{2} = 12321, 11^{2} = 121, 1^{2} = 1}
\ A = B
Example
P = {1(1 + 1), 2 (2 + 1), 3 (3 + 1), . . . . . . . 8 (8 + 1)}
Q = { 9^{2}  9, 8^{2}  8, 7^{2} 7, . . . . . . . . . 2^{2}  2 }
State whether P Ì Q or Q Ì P or P = Q
Solution :
P = {2, 6, 12, . . . . . . .72} , Q = { 72, 56, 42, . . . . ..2} \ P = Q

Index
2.1 Sets
2.2 Operations on Sets
2.3 The Algebra of Sets
Chapter 3
