Algebra II - 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:

$B\cap C$

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

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

$\left { 40, 60 \right }$

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

$\left { 20, 40 \right }$

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

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:

$A\cup B\cup C$

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

$\left { 40, 60 \right }$

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

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

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

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.

Sets3

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

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 , and set F contains terms . Therefore, the union of these two sets is .

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:

$A\cap B\cap C$

$\left { 20, 40 \right }$

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

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

$\left { 40 \right }$

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

Explanation

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

Set A is composed of all multiples of 4 that are that are less than the square of 7. Set B includes all multiples of 6 that are greater than 0. How many numbers are found in both set A and set B?

Explanation

Start by making a list of the multiples of 4 that are smaller than the square of 7. When 7 is squared, it equals 49; thus, we can compose the following list:

$\text{4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48}$

Next, make a list of all the multiples of 6 that are greater than 0. Since we are looking for shared multiples, stop after 48 because numbers greater than 48 will not be included in set A. The biggest multiple of 4 smaller that is less than 49 is 48; therefore, do not calculate multiples of 6 greater than 48.

$\text{6, 12, 18, 24, 30, 36, 42, and 48}$

Finally, count the number of multiples found in both sets. Both sets include the following numbers:

$\text{12, 24, 36, and 48}$

The correct answer is 4 numbers.

True or false:

The following set comprises only imaginary numbers:

$\left { i^{7}, i^{9}, i^{11}, i^{13}, i^{15}\right }$

True

False

Explanation

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Powers of i

Every element in the set $\left { i^{7}, i^{9}, i^{11}, i^{13}, i^{15}\right }$ is equal to raised to an odd-numbered power, so when each exponent is divided by 4, the remainder will be either 1 or 3. Therefore, each element is equal to either or . Consequently, the set includes only imaginary numbers.

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:

$A\cap B$

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

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

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

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

$\left { 20, 40 \right }$

Explanation

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

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:

$A\cup B$

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

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

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

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

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

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