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Algebra II : Number Sets

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Example Question #1 : Number Sets

If $A= \left \{ 10, 20, 30, 40, 50 \right \}$ , $B=\left \{ 10, 20, 40, 60 \right \}$ , and $C=\left \{ 20, 30, 40, 60 \right \}$ , then find the following set:

$A\cup B$

Possible Answers:

$\left \{ 10, 20, 30, 40, 50 \right \}$

$\left \{ 10, 20, 40 \right \}$

$\left \{ 10, 20, 40, 50, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$

Correct answer:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

Explanation:

The union is the set that contains all the numbers from $A= \left \{ 10, 20, 30, 40, 50 \right \}$ and $B=\left \{ 10, 20, 40, 60 \right \}$ . Therefore the union is $\left \{ 10, 20, 30, 40, 50, 60 \right \}$ .

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Example Question #2 : Number Sets

If $A= \left \{ 10, 20, 30, 40, 50 \right \}$ , $B=\left \{ 10, 20, 40, 60 \right \}$ , and $C=\left \{ 20, 30, 40, 60\right \}$ , find the following set:

$A\cap B\cap C$

Possible Answers:

$\left \{ 40 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 20, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$

$\left \{ 20, 30, 40 \right \}$

Correct answer:

$\left \{ 20, 40 \right \}$

Explanation:

The intersection is the set that contains only the numbers found in all three sets. Therefore the intersection is $\left \{ 20, 40 \right \}$ .

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Example Question #1 : Number Sets

If $A= \left \{ 10, 20, 30, 40, 50 \right \}$ , $B=\left \{ 10, 20, 40, 60 \right \}$ , and $C=\left \{ 20, 30, 40, 60 \right \}$ , find the following set:

$B\cap C$

Possible Answers:

$\left \{ 10, 20, 40, 60 \right \}$

$\left \{ 40, 60 \right \}$

$\left \{ 20, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$

$\left \{10, 20, 40 \right \}$

Correct answer:

$\left \{ 20, 40, 60 \right \}$

Explanation:

The intersection is the set that contains the numbers that appear in both $B=\left \{ 10, 20, 40, 60 \right \}$ and $C=\left \{ 20, 30, 40, 60 \right \}$ . Therefore the intersection is $\left \{ 20, 40, 60 \right \}$ .

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Example Question #4 : Number Sets

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ , $B=\left \{ 10, 20, 40, 60 \right \}$ , and $C=\left \{ 20, 30, 40, 60 \right \}$ , find the following set:

$A\cap C$

Possible Answers:

$\left \{ 20, 30, 40 \right \}$

$\left \{ 30, 40 \right \}$

$\left \{ 20, 40 \right \}$

$\left \{ 20, 30, 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

Correct answer:

$\left \{ 20, 30, 40 \right \}$

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is $\left \{ 20, 30, 40 \right \}$ .

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Example Question #5 : Number Sets

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ , $B=\left \{ 10, 20, 40, 60 \right \}$ , and $C=\left \{ 20, 30, 40, 60\right \}$ , find the following set:

$A\cup B\cup C$

Possible Answers:

$\left \{ 10, 20, 30, 40, 50 \right \}$

$\left \{ 40, 60 \right \}$

$\left \{ 20, 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$

Correct answer:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

Explanation:

The union is the set that contains all of the numbers found in all three sets. Therefore the union is $\left \{ 10, 20, 30, 40, 50, 60 \right \}$ . You do not need to re-write the numbers that appear more than once.

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Example Question #6 : Number Sets

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ , $B=\left \{ 10, 20, 40, 60\right \}$ , and $C=\left \{ 20, 30, 40, 60\right \}$ , find the following set:

$A\cap B$

Possible Answers:

$\left \{ 10, 20, 40 \right \}$

$\left \{ 20, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$

Correct answer:

$\left \{ 10, 20, 40 \right \}$

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is $\left \{ 10, 20, 40 \right \}$ .

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Example Question #1 : Number Sets

Sets3

Which set of numbers represents the union of E and F?

Possible Answers:

35,60,15,70,250

60,15,75,140,250,70

70,15

{35,70,15,60,75,250}

70,15,60,75

Correct answer:

{35,70,15,60,75,250}

Explanation:

The union is the set of numbers that lie in set E or in set F.

. Sets3

In this problem set E contains terms 35,60,15,70 , and set F contains terms 250,70,15,75 . Therefore, the union of these two sets is 35,60,15,70,75,250 .

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Example Question #8 : Number Sets

Express the following in Set Builder Notation:

$\left ( -\infty , -3\ \right )\cup \left ( -3, 1 \right )\cup \left ( 1, \infty \right )$

Possible Answers:

$\left \{ x|-\infty < x< -3 \right \}$

$\left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$

$\left \{ x|-3< x< \infty \right \}$

$\left \{ x|-\infty < x< 1 \right \}$

$\left \{ x|-3< x< 1 \right \}$

Correct answer:

$\left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$

Explanation:

$\left ( -\infty , -3 \right ) = \left \{x| -\infty < x< -3 \right \}$

and $\cup$ stands for OR in Set Builder Notation

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Example Question #1 : Number Sets

Find the intersection of the two sets:

$A=\left \{ 1, 2, 3, 4, 5, 6, 7, 8 \right \}, B=\left \{ 2, 4, 6, 7, 9 \right \}$

Possible Answers:

$\left \{ 1, 2, 3, 4, 5, 6, 7, 8,9 \right \}$

$\left \{ \right \}$

$\left \{ 1, 3, 5, 8, 9 \right \}$

$\left \{ 2, 4, 6, 7 \right \}$

Correct answer:

$\left \{ 2, 4, 6, 7 \right \}$

Explanation:

To find the intersection of the two sets, $A\cap B$ , we must find the elements that are shared by both sets:

$\left \{ 2, 4, 6, 7 \right \}$

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Example Question #1 : Number Sets

What type of numbers are contained in the set [3, 6, -4, 0, 8] ?

Possible Answers:

Complex

Irrational

Natural

Integers

Imaginary

Correct answer:

Integers

Explanation:

We can use process of elimination to find the correct answer.

It can't be Imaginary because we're not dividing by a negative number.

It can't be Complex because the number's aren't a mix of real and imaginary numbers.

It can't be Irrational because they aren't fractions.

It can't be Natural because there are negative numbers.

It must be Integers then! All the numbers are whole numbers that fit on the number line.

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Algebra II : Number Sets

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Number Sets

Example Question #2 : Number Sets

Example Question #1 : Number Sets

Example Question #4 : Number Sets

Example Question #5 : Number Sets

Example Question #6 : Number Sets

Example Question #1 : Number Sets

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Example Question #1 : Number Sets

Example Question #1 : Number Sets

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