# 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.

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a B

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https://brainmass.com/math/discrete-math/determine-the-number-of-subsets-403403

#### 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.

Compare improper and proper subsets.

Sets (Part I)

1. List all the subsets of { 8, 16, 27, 31, 60}

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)

5. Use the Venn diagram to list the set of elements in roster form. Find A â?ª B.

Assignment Expectations:

Clearly define sets and set operations.

Select appropriate set elements and distinquish between sets, subsets, and proper subsets.

Sets (Part II)

Also, for the first SLP I want you to put into practice what you have learned about sets and functions. I want you to create three sets, set A, set B, and set C by going through the items you use at work (or in your field).

Set A will be a list of all of these items.

Create Set B, from the items in Set A that you think are essential.

Create Set C, by taking the complement of Set B in Set A, i.e. all of the non-essential items.

Are sets B and C proper subsets of set A? Explain.

Submit a one to two page paper with this information along with Part I of SLP by the end of this module.

Assignment Expectations:

Identify a set and elements of the set that would make up subsets. from the original set.

Distinguish between improper and proper subsets.

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