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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 =     26 = 64

4) n (B) = 3 Þ 23 = 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 = { 11112 , 1112, 112, 12 }

State whether A Ì B or B Ì A or A = B

Solution :

Now B = {11112 = 1234321, 1112 = 12321, 112 = 121,
12 = 1}

\ A = B

Example

P = {1(1 + 1), 2 (2 + 1), 3 (3 + 1), . . . . . . . 8 (8 + 1)}

Q = { 92 - 9, 82 - 8, 72- 7, . . . . . . . . . 22 - 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