Question

Determine the power set for T = {elm, pine, oak}.

P(T) = {{elm}, {pine}, {oak}, {elm, pine}, {elm, oak}, {pine, oak}}
P(T) = {{elm}, {pine}, {oak}, {elm, pine, oak}}
P(T) = {{ }, {elm}, {pine}, {oak}, {elm, pine}, {elm, oak}, {pine, oak}, {elm, pine, oak}, {elm, pine, oak, palm}}
P(T) = {{ }, {elm}, {pine}, {oak}, {elm, pine}, {elm, oak}, {pine, oak}, {elm, pine, oak}}

Answer 1

The power set for T = {elm, pine, oak} is:

c. P(T) = {{ }, {elm}, {pine}, {oak}, {elm, pine}, {elm, oak}, {pine, oak}, {elm, pine, oak}, {elm, pine, oak, palm}}

This is because the power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. In this case, T has 3 elements, so there are 2^3 = 8 possible subsets. These are:

- The empty set {}
- The singleton sets {elm}, {pine}, and {oak}
- The doubleton sets {elm, pine}, {elm, oak}, and {pine, oak}
- The set T itself {elm, pine, oak}

Option c lists all of these subsets, including the empty set and the set T.