2 list all partitions of the set S abcd SolutionA partition

2. list all partitions of the set S = {a,b,c,d}.

Solution

A partition of a set S is a sub division of the set into sub sets that are disjoint and exhaustive that is every element of S must belongs to one and only one of the sub sets.

Here S= {a, b, c, d}

We can partitions S in the following ways

1. { {a}, {b}, {c}, {d}} Here all sub sets are single and no common elements.

2. { {a,b}, {c,d}} Here all sub sets are contains two elements and sub sets are no common elements.

3 {{a,c}, {b, d}} two sub sets having two elements and no common elements

4.{{a,d}, {b,c}} two sub sets having two elements and no common elements. similarly we can get

5. {{a,b,c},{d}}

6.{{a,b.d} , {c}}

7.{{a,c,d}, {b}}

8. {{b,c,d},{a}}

9.{{a},{b},{c,d}}

10.{{a},{c},{b,d}}

11.{{a},{d},{b,c}}

12.{{b},{c},{a,d}}

13.{{c},{d},{a,b}}