Hey guys, I am just starting this new topic, and I have been finding it really confusing. I have an assignment due and I was wondering if someone could help me solve these problems? Thanks!
List all the subsets of each set.
-I have been having trouble finding the subsets for the following problems. Anyone have some tips or some start to help me into the right direction?
1. {0, 1}
2. {-4, 0, 4}
3. {w, x, y, z}
If someone could help me out that would be great. I'm falling behind on my math due to this assignment and I really want some time off for Thanksgiving break. Anyone that could help as soon as they can would be great. Thanks! :D
P.S. These aren't to a quiz or test, so I'm not trying to cheat and look for complete answers. I was just hoping someone could guide me on how to work these out.
- Lupa
These are to a worksheet assignment :)
The set of all subsets is called the power set. A set with n elements has 2^n subsets.
For example, the list of subsets of
{0,1} is {},{0},{1},{0,1}
You can think of it as listing all the binary numbers from 0 to N, then selecting those elements that correspond to a 1 in the digit. For example,
If a set has 3 elements, then for #2 above, with the set {-4,0,4}
000 : {}
001 : {4)
010 : {0}
011 : {0,4}
100 : {-4}
101 : {-4,4}
110 : {-4,0}
111 : {-4,0,4}
Hi Lupa! I'd be happy to help you with your assignment. Let's start by discussing what subsets are.
A subset of a set is a collection of elements from that set. In other words, it is a smaller set that is formed by choosing some or all of the elements from the original set.
To find all the subsets of a set, you can use a method called the "power set" method. The power set of a set is simply the set of all possible subsets.
Now, let's work through the three sets you provided and find their subsets:
1. {0, 1}
To find the subsets of this set, you can consider each element and decide whether to include it or not. Let's go step by step:
- The empty set {} is a subset of any set, so that is one of the subsets.
- Next, consider the element 0. You can either include it or not. So we have two subsets: {0} and {}.
- Similarly, for the element 1, we have two subsets: {1} and {}.
- And finally, we have the original set itself: {0, 1}.
So, the subsets of {0, 1} are: {}, {0}, {1}, and {0, 1}.
2. {-4, 0, 4}
Again, we will go through each element and decide whether to include it or not:
- The empty set {} is always a subset.
- For the element -4, we can either include it or not. So we have two subsets: {-4} and {}.
- For the element 0, we have two subsets: {0} and {}.
- For the element 4, we have two subsets: {4} and {}.
- Now, we can combine the elements. For example, combining {-4} and {0}, we have {-4, 0}. Doing this for all possible combinations, we get the following subsets: {}, {-4}, {0}, {4}, {-4, 0}, {-4, 4}, {0, 4}, and {-4, 0, 4}.
So, the subsets of {-4, 0, 4} are: {}, {-4}, {0}, {4}, {-4, 0}, {-4, 4}, {0, 4}, and {-4, 0, 4}.
3. {w, x, y, z}
Following the same process:
- The empty set {} is always a subset.
- For the element w, we can either include it or not. So we have two subsets: {w} and {}.
- For the element x, we have two subsets: {x} and {}.
- For the element y, we have two subsets: {y} and {}.
- For the element z, we have two subsets: {z} and {}.
- Combining the elements, we get: {}, {w}, {x}, {y}, {z}, {w, x}, {w, y}, {w, z}, {x, y}, {x, z}, {y, z}, {w, x, y}, {w, x, z}, {w, y, z}, {x, y, z}, and {w, x, y, z}.
So, the subsets of {w, x, y, z} are: {}, {w}, {x}, {y}, {z}, {w, x}, {w, y}, {w, z}, {x, y}, {x, z}, {y, z}, {w, x, y}, {w, x, z}, {w, y, z}, {x, y, z}, and {w, x, y, z}.
I hope this helps! If you have any further questions or need clarification, feel free to ask.