Mathematics Homework Help

I’m working on a mathematics question and need an explanation and answer to help me learn.

2. Let S = {1,2,3,…,18,19,20} be the universal set.

Let sets A and B be subsets of S, where:

Set $A=\{1,2,12,13,14,16,17,18\}$

Set $B=\{2,3,4,6,7,13,15,16,17,19,20\}$

LIST the elements in Set A and Set B: { }

LIST the elements in Set A or Set B: { }

Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

You may want to draw a Venn Diagram to help answer this question.

3.Let $U=${1,2,3,…,10}, $A=${1,3,5,7}, $B=${1,2,3,4}, and $C=${3,4,6,7,9}.

Select $A^c$

$A^c$ from the choices below.

• {2,3,4,5,7,9}
• {2,4,6,8,9,10}
• {2,4,5,7,8,9}
• {1,5,6,7,8,9}
• {2,3,4,5,7,9}
• $\varnothing$

4. Let $S$ be the universal set, where:
$S=\{1,2,3,\dots ,18,19,20\}$
Let sets $A$ and $B$ be subsets of $S$, where:

Set $A=\{1,3,6,7,8,11,12,14,16,17,19,20\}$

$A=\{1,3,6,7,8,11,12,14,16,17,19,20\}$

Set $B=\{1,2,3,5,6,7,13,18\}$

$B=\{1,2,3,5,6,7,13,18\}$

Find the following:

LIST the elements in the set ($A\cup B$

$A\cup B$):
$(A\cup B)$ = { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

LIST the elements in the set ($A\cap B$

$A\cap B$):
$(A\cap B)$ = { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

You may want to draw a Venn Diagram to help answer this question.

5.Let $S=\{1,2,3,4,5,6,7,8,9,10\}$ be the universal set.

Let sets $A$

$A$, $B$, and $C$ be subsets of $S$, where:

Set $A=\{1,5,7,9,10\}$

$A=\{1,5,7,9,10\}$

Set $B=\{1,3,10\}$

$B=\{1,3,10\}$

Set $C=\{3,4,6,9\}$

$C=\{3,4,6,9\}$

LIST the elements in the set $A\cap B\cap C$

$A\cap B\cap C$:
$A\cap B\cap C$ = { }

LIST the elements in the set $A\cup B\cup C$

$A\cup B\cup C$:
$A\cup B\cup C$ = { }

Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

6.Suppose you have 14 tubes of paint. How many distinct color groupings can you make with your paint?

7.Let $U$ be the universal set, where:
$U=\{a,b,c,d,e,f,g,h\}$
Let sets $A$, $B$, and $C$ be subsets of $U$, where:

$A=\{a,c,e,f,g\}$

$A=\{a,c,e,f,g\}$

$B=\{a,b,c,f,g,h\}$

$B=\{a,b,c,f,g,h\}$

$C=\{a,c,d,f\}$

$C=\{a,c,d,f\}$

Complete a Venn diagram for the sets and then answer the question following.

[Graphs generated by this script: initPicture(-6.5,6.5,-5.5,5.5);circle([0,-1.7],3);circle([2,2],3);circle([-2,2],3);fontbackground=’white’;text([-4.5,4.5],’A’);text([4.5,4.5],’B’);text([-2.2,-4.5],’C’);text([6.2,5],’U’);]

List the elements in the set ${(A\cap C)}^{\prime }\cup {(B\cap A)}^{\prime }$

}
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

8.The Venn diagram below shows the number of people in a room labeled with their like of cats and/or dogs.

Cats

Dogs

12

5

13

16

How many people like cats?
How many people don’t like cats?
How many people like dogs?
How many people don’t like dogs?
How many people like cats and dogs?
How many people like dogs but not cats?
How many people are in the room?

9.A survey asks “What beverage do you drink in the morning”, and offers choices:

– Tea only
– Coffee only
– Both coffee and tea
– Neither coffee nor tea

The results are presented in the following Venn Diagram.

10

32

20

33

How many people drink only tea in the morning? people

How many people drink tea in the morning?

people

How many people do not drink tea?

people

How many people were surveyed?

people