I have trouble with remembering sets. So these are my questions, and can someone show me how to do them?
(1)Z is the set of all letters of the alphabet. Z={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}
(a) A is a subset of set Z. A= {a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, p, q, r, s, t}. What is Aβ?
(b) B= {w, x, y}. What are all of the subsets of set B?
(c) What is the set of π¨ βͺ π©?
(d) What is the set of π¨ β© π©?
I want to do the work myself but I just need the steps!
A' is all the letters in Z but not in A
B has 8 subsets, consisting of any possible combinations of elements of B (including none or all of them)
Since B is a subset of A, AUB = A
similarly, Aβ©B = B
better read up on union and intersection
Sure! I'll guide you through the steps to find the answers to your questions.
(a) To find the complement of set A, denoted by A', we need to identify all the elements in the universal set (set Z) that are not in set A.
1. Start with the universal set Z and list down all the elements {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}.
2. Compare this list with the elements in set A, which are {a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, p, q, r, s, t}.
3. Cross out any elements from the universal set that exist in set A. The remaining elements will constitute set A'.
4. The complement of set A, A', is {u, v, w, x, y, z}.
(b) To find all the subsets of set B, you can follow these steps:
1. Recall that a subset is a set that contains some or all of the elements of the original set, including the empty set and the set itself.
2. Begin by listing all the unique elements in set B, which are {w, x, y}.
3. Create subsets by considering all possible combinations of these elements.
- Subset 1: {} (empty set)
- Subset 2: {w}
- Subset 3: {x}
- Subset 4: {y}
- Subset 5: {w, x}
- Subset 6: {w, y}
- Subset 7: {x, y}
- Subset 8: {w, x, y}
4. Hence, the subsets of set B are: {}, {w}, {x}, {y}, {w, x}, {w, y}, {x, y}, {w, x, y}.
(c) To find the union of sets A and B (A βͺ B), follow these steps:
1. List down all the unique elements in set A, which are {a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, p, q, r, s, t}.
2. List down all the unique elements in set B, which are {w, x, y}.
3. Combine the elements from sets A and B, removing any duplicates.
4. The union of sets A and B, A βͺ B, is {a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, p, q, r, s, t, w, x, y}.
(d) To find the intersection of sets A and B (A β© B), follow these steps:
1. List down all the unique elements in set A, which are {a, b, c, d, e, f, g, h, I, j, k, l, m, n, o, p, q, r, s, t}.
2. List down all the unique elements in set B, which are {w, x, y}.
3. Identify the elements that exist in both sets.
4. The intersection of sets A and B, A β© B, is {}. (In this case, set A and set B have no common elements.)
I hope these step-by-step instructions help you work through the problems! Let me know if you have any further questions.