Solved on Feb 18, 2024

Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.
$A \cup B$ is: a. $\{3,4,5\}$ b. $\{3\}$ c. $\{1,2,3,4,5,6\}$ d. $\{2,3,4,5\}$

STEP 1

Assumptions
1. The sample space $S$ is $\{1,2,3,4,5,6\}$ .
2. Set $A$ is $\{2,3\}$ .
3. Set $B$ is $\{3,4,5\}$ .
4. We are looking for the union of sets $A$ and $B$ , denoted as $A \cup B$ .

STEP 2

The union of two sets $A$ and $B$ , denoted as $A \cup B$ , is the set of elements that are in $A$ , or in $B$ , or in both.

STEP 3

List all the unique elements that are in set $A$ .
$A = \{2,3\}$

STEP 4

List all the unique elements that are in set $B$ .
$B = \{3,4,5\}$

STEP 5

Combine all the unique elements from sets $A$ and $B$ to form the union $A \cup B$ .

STEP 6

When combining the elements, remember that each element should only appear once in the union, even if it appears in both sets.

STEP 7

Write down the union of sets $A$ and $B$ .
$A \cup B = \{2,3,4,5\}$

STEP 8

Compare the result with the given options to find the correct one.
The correct answer is: $A \cup B = \{2,3,4,5\}$
This corresponds to option d. $\{2,3,4,5\}$ .

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Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.
$A \cup B$ is: a. $\{3,4,5\}$ b. $\{3\}$ c. $\{1,2,3,4,5,6\}$ d. $\{2,3,4,5\}$

STEP 1

Assumptions
1. The sample space $S$ is $\{1,2,3,4,5,6\}$ .
2. Set $A$ is $\{2,3\}$ .
3. Set $B$ is $\{3,4,5\}$ .
4. We are looking for the union of sets $A$ and $B$ , denoted as $A \cup B$ .

STEP 2

The union of two sets $A$ and $B$ , denoted as $A \cup B$ , is the set of elements that are in $A$ , or in $B$ , or in both.

STEP 3

List all the unique elements that are in set $A$ .
$A = \{2,3\}$

STEP 4

List all the unique elements that are in set $B$ .
$B = \{3,4,5\}$

STEP 5

Combine all the unique elements from sets $A$ and $B$ to form the union $A \cup B$ .

STEP 6

When combining the elements, remember that each element should only appear once in the union, even if it appears in both sets.

STEP 7

Write down the union of sets $A$ and $B$ .
$A \cup B = \{2,3,4,5\}$

STEP 8

Compare the result with the given options to find the correct one.
The correct answer is: $A \cup B = \{2,3,4,5\}$
This corresponds to option d. $\{2,3,4,5\}$ .

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Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.A∪BA \cup BA∪B is: a. {3,4,5}\{3,4,5\}{3,4,5} b. {3}\{3\}{3} c. {1,2,3,4,5,6}\{1,2,3,4,5,6\}{1,2,3,4,5,6} d. {2,3,4,5}\{2,3,4,5\}{2,3,4,5}

STEP 1

Assumptions1. The sample space SSS is {1,2,3,4,5,6}\{1,2,3,4,5,6\}{1,2,3,4,5,6}.2. Set AAA is {2,3}\{2,3\}{2,3}.3. Set BBB is {3,4,5}\{3,4,5\}{3,4,5}.4. We are looking for the union of sets AAA and BBB, denoted as A∪BA \cup BA∪B.

STEP 2

The union of two sets AAA and BBB, denoted as A∪BA \cup BA∪B, is the set of elements that are in AAA, or in BBB, or in both.

STEP 3

List all the unique elements that are in set AAA.A={2,3}A = \{2,3\}A={2,3}

STEP 4

List all the unique elements that are in set BBB.B={3,4,5}B = \{3,4,5\}B={3,4,5}

STEP 5

Combine all the unique elements from sets AAA and BBB to form the union A∪BA \cup BA∪B.

STEP 6

When combining the elements, remember that each element should only appear once in the union, even if it appears in both sets.

STEP 7

Write down the union of sets AAA and BBB.A∪B={2,3,4,5}A \cup B = \{2,3,4,5\}A∪B={2,3,4,5}

STEP 8

Compare the result with the given options to find the correct one.The correct answer is: A∪B={2,3,4,5}A \cup B = \{2,3,4,5\}A∪B={2,3,4,5}This corresponds to option d. {2,3,4,5}\{2,3,4,5\}{2,3,4,5}.

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Find the union of sets A and B given a sample space S = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}.
$A \cup B$ is: a. $\{3,4,5\}$ b. $\{3\}$ c. $\{1,2,3,4,5,6\}$ d. $\{2,3,4,5\}$

Assumptions
1. The sample space $S$ is $\{1,2,3,4,5,6\}$ .
2. Set $A$ is $\{2,3\}$ .
3. Set $B$ is $\{3,4,5\}$ .
4. We are looking for the union of sets $A$ and $B$ , denoted as $A \cup B$ .

The union of two sets $A$ and $B$ , denoted as $A \cup B$ , is the set of elements that are in $A$ , or in $B$ , or in both.

List all the unique elements that are in set $A$ .
$A = \{2,3\}$

List all the unique elements that are in set $B$ .
$B = \{3,4,5\}$

Combine all the unique elements from sets $A$ and $B$ to form the union $A \cup B$ .

Write down the union of sets $A$ and $B$ .
$A \cup B = \{2,3,4,5\}$

Compare the result with the given options to find the correct one.
The correct answer is: $A \cup B = \{2,3,4,5\}$
This corresponds to option d. $\{2,3,4,5\}$ .