QuestionDetermine if sets $A=\{5,5,5,7,7,9,9,9\}$ and $B=\{9,7,5\}$ are equivalent and equal. Explain your answers.

Studdy Solution

STEP 1

Assumptions1. The set A is {5,5,5,7,7,9,9,9} . The set B is {9,7,5} 3 sets are equivalent if they have the same number of elements4. The sets are equal if they have the exact same elements

STEP 2

First, we need to find the number of elements in each set. In set theory, the number of elements in a set is denoted by n(A) for set A and n(B) for set B.
$n(A) = \text{number of elements in set A}$ $n(B) = \text{number of elements in set B}$

STEP 3

Now, count the number of elements in set A.
$n(A) =8$

STEP 4

Count the number of elements in set B.
$n(B) =3$

STEP 5

Now that we have the number of elements in each set, we can compare them to determine if the sets are equivalent. Sets are equivalent if they have the same number of elements.
$n(A) = n(B)$

STEP 6

Plug in the values for n(A) and n(B) to check if the sets are equivalent.
$8 =3$

STEP 7

Since does not equal3, the sets are not equivalent. So, the answer to part a is The sets are not equivalent because $n(A) \neq n(B)$ .

STEP 8

Next, we need to determine if the sets are equal. Sets are equal if they contain the exact same elements.

STEP 9

Compare the elements in set A and set B.

STEP 10

Since set A contains multiple instances of the numbers5,7, and9, and set B only contains one instance of each, the sets are not equal. So, the answer to part b is The sets are not equal because set A does not contain the exact same elements as set B.

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QuestionDetermine if sets $A=\{5,5,5,7,7,9,9,9\}$ and $B=\{9,7,5\}$ are equivalent and equal. Explain your answers.

Studdy Solution

STEP 1

Assumptions1. The set A is {5,5,5,7,7,9,9,9} . The set B is {9,7,5} 3 sets are equivalent if they have the same number of elements4. The sets are equal if they have the exact same elements

STEP 2

First, we need to find the number of elements in each set. In set theory, the number of elements in a set is denoted by n(A) for set A and n(B) for set B.
$n(A) = \text{number of elements in set A}$ $n(B) = \text{number of elements in set B}$

STEP 3

Now, count the number of elements in set A.
$n(A) =8$

STEP 4

Count the number of elements in set B.
$n(B) =3$

STEP 5

Now that we have the number of elements in each set, we can compare them to determine if the sets are equivalent. Sets are equivalent if they have the same number of elements.
$n(A) = n(B)$

STEP 6

Plug in the values for n(A) and n(B) to check if the sets are equivalent.
$8 =3$

STEP 7

Since does not equal3, the sets are not equivalent. So, the answer to part a is The sets are not equivalent because $n(A) \neq n(B)$ .

STEP 8

Next, we need to determine if the sets are equal. Sets are equal if they contain the exact same elements.

STEP 9

Compare the elements in set A and set B.

STEP 10

Since set A contains multiple instances of the numbers5,7, and9, and set B only contains one instance of each, the sets are not equal. So, the answer to part b is The sets are not equal because set A does not contain the exact same elements as set B.

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QuestionDetermine if sets A={5,5,5,7,7,9,9,9}A=\{5,5,5,7,7,9,9,9\}A={5,5,5,7,7,9,9,9} and B={9,7,5}B=\{9,7,5\}B={9,7,5} are equivalent and equal. Explain your answers.

Studdy Solution

STEP 1

Assumptions1. The set A is {5,5,5,7,7,9,9,9} . The set B is {9,7,5} 3 sets are equivalent if they have the same number of elements4. The sets are equal if they have the exact same elements

STEP 2

STEP 3

Now, count the number of elements in set A.n(A)=8n(A) =8n(A)=8

STEP 4

Count the number of elements in set B.n(B)=3n(B) =3n(B)=3

STEP 5

Now that we have the number of elements in each set, we can compare them to determine if the sets are equivalent. Sets are equivalent if they have the same number of elements.n(A)=n(B)n(A) = n(B)n(A)=n(B)

STEP 6

Plug in the values for n(A) and n(B) to check if the sets are equivalent.8=38 =38=3

STEP 7

Since does not equal3, the sets are not equivalent. So, the answer to part a is The sets are not equivalent because n(A)≠n(B)n(A) \neq n(B)n(A)=n(B).

STEP 8

Next, we need to determine if the sets are equal. Sets are equal if they contain the exact same elements.

STEP 9

Compare the elements in set A and set B.

STEP 10

Since set A contains multiple instances of the numbers5,7, and9, and set B only contains one instance of each, the sets are not equal. So, the answer to part b is The sets are not equal because set A does not contain the exact same elements as set B.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDetermine if sets $A=\{5,5,5,7,7,9,9,9\}$ and $B=\{9,7,5\}$ are equivalent and equal. Explain your answers.

Now, count the number of elements in set A.
$n(A) =8$

Count the number of elements in set B.
$n(B) =3$

Now that we have the number of elements in each set, we can compare them to determine if the sets are equivalent. Sets are equivalent if they have the same number of elements.
$n(A) = n(B)$

Plug in the values for n(A) and n(B) to check if the sets are equivalent.
$8 =3$

Since does not equal3, the sets are not equivalent. So, the answer to part a is The sets are not equivalent because $n(A) \neq n(B)$ .