Solved on Nov 01, 2023

For a set $U=\{5,6,7,8,9\}$ , find the complement of $A=\{5,8,9\}$ and the set $B$ given its complement $B'=\{5,6,9\}$ .
(a) $A' = \{6,7\}$ (b) $B = \{7,8\}$

STEP 1

Assumptions1. The universal set is $=\{5,6,7,8,9\}$ . The set $A=\{5,8,9\}$
3. The complement of set $B$ , denoted as $B^{\prime}$ , is $\{5,6,9\}$
4. The complement of a set is the set of all elements in the universal set that are not in the given set.

STEP 2

To find the complement of set $A$ , denoted as $A^{\prime}$ , we need to find all the elements in the universal set $$ that are not in set $A$.
$A^{\prime} = U - A$

STEP 3

Now, plug in the given values for the universal set $$ and set $A$ to calculate $A^{\prime}$.
$A^{\prime} = \{5,6,7,8,9\} - \{5,8,9\}$

STEP 4

Calculate the set $A^{\prime}$ .
$A^{\prime} = \{6,7\}$

STEP 5

To find the set $B$ , given that $B^{\prime}=\{5,,9\}$ , we need to find all the elements in the universal set $$ that are not in set $B^{\prime}$.
$B = U - B^{\prime}$

STEP 6

Now, plug in the given values for the universal set $$ and set $B^{\prime}$ to calculate $B$.
$B = \{5,6,,8,9\} - \{5,6,9\}$

STEP 7

Calculate the set $B$ .
$B = \{7,\}$ So, the complement of set $A$ is $\{6,7\}$ and set $B$ is $\{7,\}$ .

Was this helpful?

For a set $U=\{5,6,7,8,9\}$ , find the complement of $A=\{5,8,9\}$ and the set $B$ given its complement $B'=\{5,6,9\}$ .
(a) $A' = \{6,7\}$ (b) $B = \{7,8\}$

STEP 1

Assumptions1. The universal set is $=\{5,6,7,8,9\}$ . The set $A=\{5,8,9\}$
3. The complement of set $B$ , denoted as $B^{\prime}$ , is $\{5,6,9\}$
4. The complement of a set is the set of all elements in the universal set that are not in the given set.

STEP 2

To find the complement of set $A$ , denoted as $A^{\prime}$ , we need to find all the elements in the universal set $$ that are not in set $A$.
$A^{\prime} = U - A$

STEP 3

Now, plug in the given values for the universal set $$ and set $A$ to calculate $A^{\prime}$.
$A^{\prime} = \{5,6,7,8,9\} - \{5,8,9\}$

STEP 4

Calculate the set $A^{\prime}$ .
$A^{\prime} = \{6,7\}$

STEP 5

To find the set $B$ , given that $B^{\prime}=\{5,,9\}$ , we need to find all the elements in the universal set $$ that are not in set $B^{\prime}$.
$B = U - B^{\prime}$

STEP 6

Now, plug in the given values for the universal set $$ and set $B^{\prime}$ to calculate $B$.
$B = \{5,6,,8,9\} - \{5,6,9\}$

STEP 7

Calculate the set $B$ .
$B = \{7,\}$ So, the complement of set $A$ is $\{6,7\}$ and set $B$ is $\{7,\}$ .

Start learning now

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

For a set U={5,6,7,8,9}U=\{5,6,7,8,9\}U={5,6,7,8,9}, find the complement of A={5,8,9}A=\{5,8,9\}A={5,8,9} and the set BBB given its complement B′={5,6,9}B'=\{5,6,9\}B′={5,6,9}.(a) A′={6,7}A' = \{6,7\}A′={6,7} (b) B={7,8}B = \{7,8\}B={7,8}

STEP 1

STEP 2

To find the complement of set AAA, denoted as A′A^{\prime}A′, we need to find all the elements in the universal set $$ that are not in set $A$.A′=U−AA^{\prime} = U - AA′=U−A

STEP 3

Now, plug in the given values for the universal set $$ and set $A$ to calculate $A^{\prime}$.A′={5,6,7,8,9}−{5,8,9}A^{\prime} = \{5,6,7,8,9\} - \{5,8,9\}A′={5,6,7,8,9}−{5,8,9}

STEP 4

Calculate the set A′A^{\prime}A′.A′={6,7}A^{\prime} = \{6,7\}A′={6,7}

STEP 5

To find the set BBB, given that B′={5,,9}B^{\prime}=\{5,,9\}B′={5,,9}, we need to find all the elements in the universal set $$ that are not in set $B^{\prime}$.B=U−B′B = U - B^{\prime}B=U−B′

STEP 6

Now, plug in the given values for the universal set $$ and set $B^{\prime}$ to calculate $B$.B={5,6,,8,9}−{5,6,9}B = \{5,6,,8,9\} - \{5,6,9\}B={5,6,,8,9}−{5,6,9}

STEP 7

Calculate the set BBB.B={7,}B = \{7,\}B={7,}So, the complement of set AAA is {6,7}\{6,7\}{6,7} and set BBB is {7,}\{7,\}{7,}.

Start learning now

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

For a set $U=\{5,6,7,8,9\}$ , find the complement of $A=\{5,8,9\}$ and the set $B$ given its complement $B'=\{5,6,9\}$ .
(a) $A' = \{6,7\}$ (b) $B = \{7,8\}$

To find the complement of set $A$ , denoted as $A^{\prime}$ , we need to find all the elements in the universal set $$ that are not in set $A$.
$A^{\prime} = U - A$

Now, plug in the given values for the universal set $$ and set $A$ to calculate $A^{\prime}$.
$A^{\prime} = \{5,6,7,8,9\} - \{5,8,9\}$

Calculate the set $A^{\prime}$ .
$A^{\prime} = \{6,7\}$

To find the set $B$ , given that $B^{\prime}=\{5,,9\}$ , we need to find all the elements in the universal set $$ that are not in set $B^{\prime}$.
$B = U - B^{\prime}$

Now, plug in the given values for the universal set $$ and set $B^{\prime}$ to calculate $B$.
$B = \{5,6,,8,9\} - \{5,6,9\}$

Calculate the set $B$ .
$B = \{7,\}$ So, the complement of set $A$ is $\{6,7\}$ and set $B$ is $\{7,\}$ .