Number Sets - Algebra 2

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

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In this problem set E contains terms , and set F contains terms . Therefore, the union of these two sets is .

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 N atural because there are negative numbers.

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

Any even power of the imaginary unit is a real number. For example,

from the definition of as the principal square root of .

Also, from the Power of a Power Property,

The intersection is the set that contains the numbers that appear in both and . Therefore the intersection is .

or A intersect B means what A and B have in common.

In this case both A and B have the numbers 1, 9, and 11.

and stands for OR in Set Builder Notation

The union is the set that contains all the numbers from and . Therefore the union is .

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.

Every element in the set 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.

The intersection is the set that contains only the numbers found in all three sets. Therefore the intersection is .

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .

The union is the set that contains all of the numbers found in all three sets. Therefore the union is . You do not need to re-write the numbers that appear more than once.

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .

To find the intersection of the two sets, , we must find the elements that are shared by both sets:

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:

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.

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

The correct answer is 4 numbers.

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

.

In this problem set E contains terms , and set F contains terms . Therefore, the union of these two sets is .

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 N atural because there are negative numbers.

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

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.

Every element in the set 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.

Any even power of the imaginary unit is a real number. For example,

from the definition of as the principal square root of .

Also, from the Power of a Power Property,

The union is the set that contains all of the numbers found in all three sets. Therefore the union is . You do not need to re-write the numbers that appear more than once.