Problem

Notice that the arrangement of numbers in each row is symmetric. See how the 4s are balanc...

Notice that the arrangement of numbers in each row is symmetric. See how the 4s are balanced in the fourth row, the 5s are balanced in the fifth row, and so on. Can you give a set theory explanation to account for this?

Example Finding All Subsets of a Set Systematically Find all subsets of the set {1, 2, 3, 4}.

We can organize this problem by considering subsets according to their size, going from 0 to 4. This method is illustrated in the following table.

Size of

Subset

Subsets of This Size

 

Number of Subsets

of This Size

0

1

1

{1}, {2}, {3}, {4}

4

2

{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}

6

3

{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}

4

4

{1, 2, 3, 4}

1

5

 

Total = 16

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