Question

Only a the brainliest can give a detailed answer explaining each step
Let S = {1,2,3,4}. The total no. of unordered pairs of disjoint subsets of S is equal to

Answer 1

Answer:

Given Below

Step-by-step explanation:

There are 16 subsets. We wish to choose pairs of these 16 subsets which share no common numbers.

If one subset is empty, the other could be any of the 15 remaining ones.

If one subset has only 1 element, then there are 4x8=32.

If one subset has 2 elements, then there are 6x4=24.

If one subset has 3 elements, then there are 4x2=8.

If one subset has 4 elements, then there is 1.

Adding the bold numbers we get 80.

HOWEVER: Each is counted twice. Now we get 40 as with the Gross Method.

This still amounted to some brutality.