List all the subsets(include the null set and the set itself.
a) (p)
b) (p,q)
c) (p,q,r)
d) (p,q,r,s)
By the way the brackets are supposed 2 b the weird curly brackets.
To list all the subsets of a set, including the null set and the set itself, you can follow these steps:
1. Start with the empty set (null set).
2. List all the elements of the given set.
3. Generate subsets by including and excluding each element in the given set.
4. Continue this process for all the elements and their combinations.
5. In the end, you will have a list of all the subsets.
Let's apply these steps to the sets you provided:
a) (p)
- Step 1: The empty set {}.
- Step 2: The set {p}.
- Step 3: (p), {}.
So the subsets of (p) are: (p) and the empty set {}.
b) (p, q)
- Step 1: The empty set {}.
- Step 2: The set {p, q}.
- Step 3: (p), (q), {}.
- Step 4: (p, q).
So the subsets of (p, q) are: (p, q), (p), (q), and the empty set {}.
c) (p, q, r)
- Step 1: The empty set {}.
- Step 2: The set {p, q, r}.
- Step 3: (p), (q), (r), {}.
- Step 4: (p, q), (p, r), (q, r).
- Step 5: (p, q, r).
So the subsets of (p, q, r) are: (p, q, r), (p, q), (p, r), (q, r), (p), (q), (r), and the empty set {}.
d) (p, q, r, s)
- Step 1: The empty set {}.
- Step 2: The set {p, q, r, s}.
- Step 3: (p), (q), (r), (s), {}.
- Step 4: (p, q), (p, r), (p, s), (q, r), (q, s), (r, s).
- Step 5: (p, q, r), (p, q, s), (p, r, s), (q, r, s).
- Step 6: (p, q, r, s).
So the subsets of (p, q, r, s) are: (p, q, r, s), (p, q, r), (p, q, s), (p, r, s), (q, r, s), (p, q), (p, r), (p, s), (q, r), (q, s), (r, s), (p), (q), (r), (s), and the empty set {}.
Hope this explanation helps! Let me know if you have any other questions.