Need help on this homework about partitions. Thanks Find out how many partitions

Question

Need help on this homework about partitions. Thanks

Find out how many partitions of {1,2,3,4} there are. One way to try to systematically find all these partitions if to find those with exactly one set in the partition, with exactly two sets in the partition and so forth. Find out how many partitions there are of {1, 2, 3, 4, 5, 6} into 3 sets where each of the three sets has 2 elements. Suppose that we have the operation * on the set A = {a, b, c, d) given by the table below: Find a partition of A = {a, b, c, d} that is not one of the two trivial partitions i.e. {{a, b, c. d}} (the partition into one set ) or the partition {{a}, {b}, {c},{d}} (the partition into one element sets) that is compatible with the operation * on A.

Explanation / Answer

1). total sets of partition= 4C1+4C2+4C3+4C4

= 2^4-1

=16-1

=15

2).total no of partiton= 6!/((2!)^3* 3!)

540

720/(8*6)

=15

3).the partiiton be

2^4-1-4-1

=10

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