List all permutations of the elements of the set {+, -, *)
List all subsets (combinations) of the elements of the set {+, -, *)
To generate all permutations and subsets of the given set {+, -, *}:
Permutations:
1. Start by choosing the first element of the permutation. There are 3 options for this: +, -, *.
2. Once you have chosen the first element, move on to the next position and choose again from the remaining elements.
3. Continue this process until you have filled all the positions.
4. Each unique combination of elements will give you a permutation.
Here are all the permutations of the set {+, -, *}:
1. +, -, *
2. +, *, -
3. -, +, *
4. -, *, +
5. *, +, -
6. *, -, +
Subsets (Combinations):
1. A subset is a selection of elements from a given set. In this case, we want to find all possible combinations of the elements {+, -, *}.
2. To generate the subsets:
- Start by selecting a subset that contains only one element. There are three possible subsets: {+}, {-}, {*}.
- Next, consider subsets with two elements. There are three choose two combinations: {+, -}, {+, *}, {-, *}.
- Finally, consider subsets with three elements. The only possible combination is {+, -, *}.
Here are all the subsets (combinations) of the set {+, -, *}:
1. {+}
2. {-}
3. {*}
4. {+, -}
5. {+, *}
6. {-, *}
7. {+, -, *}
Note: The number of subsets and permutations can be calculated using combinatorial mathematics formulas.