2. Determine the number of subsets of {mom, dad, son, daughter}

3. At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar cheese, cucumbers, onions, red peppers, hot peppers }. How many different variations are there for ordering a salad?

5. Use the Venn diagram to list the set of elements in roster form. Find A â?ª B.
u h e b
a B
n j u
m

Solution Preview

1. First remember that the empty set, {}, and the set itself, {8,16,27,31}, are subsets. Next, list all possible one element subsets: {8},{16},{27},{31}. Next, list all possible subsets with 2 elements.
{8,16}, {8,27},{8,31},{16,27},{16,31},{27,31}. (Notice that {8,16} is the same thing as {16,8}. We only want to list each subset once.)
Now, list all subsets with 3 elements: {8,16,27},{8,16,31},{8,27,31},{16,27,31}.

Notice that there are 2^4 = 16 subsets. In ...

Solution Summary

A series of problems related to sets, subsets, unions, and intersections are given. The solutions use set notation and Venn Diagrams and include explanations for determining how many subsets can be made from a set with a given number of elements.

Hello,
I have another discrete problem I need help on.
It says: How many subsets contain 1 or 2 or 3 in the set {1,2,...,20}?
So my teacher told me that {1} is a subset, {1,3,4,5,19} would be a subset (i just chose that randomly), {2} would be a subset, {2,5,6,7,20} would be a subset (again, i just chose that at random

1. Without writing them all out, what is thenumber of subsets of set A ={king, queen, knight, prince, princess, duke}?
2. Given these elements of sets A, B, and C list the elements of set D. Show your work step by step.
A = {1, 2, 3, 4}
B = {3, 4, 5, 6, 7}
C = {3, 5, 7, 9}
D = A intersected with (B U C)

The Complement A of an r-subset A of {1,2...,n} is the (n-r)-subset of {1,2,...,n} consisting of all those elements that do not belong to A. Let M= C(n,r), thenumber of r subsets and at the same time thenumber of (n-r)-subsets of {1,2...,n}. Prove that if A1,A2,A3...AM are the r subsets in lexigraphic order then complements Am

(a) List all subsets of the set {a, b, c, d}.
(b) Determinethenumber of subsets of the set A = {a, b, c, d, e, f}, without writing them down.
(c) Determinethenumber of subsets of the set B = {a, b, c, d, e, f, g, h, i} , without writing them down.

Let S be a finite set on which a group G operates transitively, and let U be a subset of S. Prove that thesubsets gU cover S evenly, that is, that every element of S is in the same number of sets gU.

Sets (Part I)
1. List all thesubsets of { 8, 16, 27, 31, 60}
2. Determinethenumber of subsets of {mom, dad, son, daughter}
3. At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar chees

Define a new metric d on X = (0, 1/2)^2 by d((a,b), (r,s)) = 1 if a is not equal to r Or |b - s| if a = r.
a) Show that d is a metric on X.
b) What are the compact subsets of X? Prove your statement.

1. Given the following sets, select the statement below that is true.
A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}
B ⊆ A and A ⊂ B
C ⊂ A and B ⊂ C
A ⊆ C and B ⊂ A
C ⊆ B and B ⊆ A
B ⊆ C and C ⊂ A
2. Without writing them all out, what is thenumber o

Note: U = union, n = intersect
1. Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}.
Determine A U (B n C)
2. Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}