l Power Set for S = {b,c,f}
Enter Set

For set S = {b,c,f}, show:

Elements, cardinality, and power set

List the elements of S

Elements = set objects
Use the ∈ symbol.

  1. b ∈ S
  2. c ∈ S
  3. f ∈ S

Cardinality of set S → |S|:

Cardinality = Number of set elements.

Since the set S contains 3 elements

|S| = 3

Determine the power set P:

Power set = Set of all subsets of S
including S and ∅.

Calculate power set subsets

S contains 3 terms
Power Set contains 23 = 8 items

Build subsets of P

The subset A of a set B is
A set where all elements of A are in B.

#BinaryUse if 1Subset
0000b,c,f{}
1001b,c,f{f}
2010b,c,f{c}
3011b,c,f{c,f}
4100b,c,f{b}
5101b,c,f{b,f}
6110b,c,f{b,c}
7111b,c,f{b,c,f}

List our Power Set P in notation form:


P = {{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}

Partition 1

{c,f},{b}

Partition 2

{b,f},

Partition 3

{b,c},

Partition 4

{{b},{c},{f})