List the subsets of {P, N, D, Q}, where Q represents a quarter. How many subsets did you find?
There are 2^n subsets of an n-element set.
What does it matter what Q is?
25 heatbeats in 20 seconds is this a unit rate or non unit rate
To list all the subsets of a set, including the set {P, N, D, Q}, follow these steps:
1. Start with an empty set ∅ as the first subset.
2. Consider each element in the original set, {P, N, D, Q}, and generate new subsets by either including or excluding each element.
3. To generate subsets that include an element, add the element to all previously generated subsets. For example, if the element is P, add P to all previously generated subsets.
4. To generate subsets that exclude an element, copy all previously generated subsets without including that element. For example, if the element is N, exclude N from all previously generated subsets.
5. Repeat step 3 and 4 for each element in the original set.
6. Combine all the subsets generated from steps 3, 4, and 5 to get the complete list of subsets.
Let's go through the steps to find all the subsets of the set {P, N, D, Q}:
1. Start with an empty set: ∅
2. Consider the first element, P:
- Include P in previously generated subsets: {P}
- Exclude P from previously generated subsets: ∅ (no elements)
So, the subsets for just the element P are: {P}, ∅
3. Consider the second element, N:
- Include N in previously generated subsets: {N}, {P, N}
- Exclude N from previously generated subsets: ∅ (no elements), {P}
So, the subsets for just the element N are: {N}, {P, N}, ∅, {P}
4. Consider the third element, D:
- Include D in previously generated subsets: {D}, {P, D}, {N, D}, {P, N, D}
- Exclude D from previously generated subsets: ∅ (no elements), {P}, {N}, {P, N}
So, the subsets for just the element D are: {D}, {P, D}, {N, D}, {P, N, D}, ∅, {P}, {N}, {P, N}
5. Consider the last element, Q:
- Include Q in previously generated subsets: {Q}, {P, Q}, {N, Q}, {P, N, Q}, {D, Q}, {P, D, Q}, {N, D, Q}, {P, N, D, Q}
- Exclude Q from previously generated subsets: ∅ (no elements), {P}, {N}, {P, N}, {D}, {P, D}, {N, D}, {P, N, D}
So, the subsets for just the element Q are: {Q}, {P, Q}, {N, Q}, {P, N, Q}, {D, Q}, {P, D, Q}, {N, D, Q}, {P, N, D, Q}, ∅, {P}, {N}, {P, N}, {D}, {P, D}, {N, D}, {P, N, D}
6. Combine all the subsets generated from steps 3, 4, and 5 to get the complete list of subsets:
∅, {P}, {N}, {P, N}, {D}, {P, D}, {N, D}, {P, N, D}, {Q}, {P, Q}, {N, Q}, {P, N, Q}, {D, Q}, {P, D, Q}, {N, D, Q}, {P, N, D, Q}
So, the list of all the subsets of the set {P, N, D, Q} is: ∅, {P}, {N}, {P, N}, {D}, {P, D}, {N, D}, {P, N, D}, {Q}, {P, Q}, {N, Q}, {P, N, Q}, {D, Q}, {P, D, Q}, {N, D, Q}, {P, N, D, Q}.
There are a total of 16 subsets.