# Determine the Number of Subsets

1. List all the subsets of { 8, 16, 27, 31}

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?

4. 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 â?© (B â?ª C)

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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

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#### 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.