Solved on Feb 12, 2024

List the elements in the set $A^{\prime} \cup B$ , where $A = \{q, s, u, w, y\}$ and $B = \{q, s, y, z\}$ .

STEP 1

Assumptions
1. $U$ is the universal set with elements $\{q, r, s, t, u, v, w, x, y, z\}$ .
2. $A$ is a subset of $U$ with elements $\{q, s, u, w, y\}$ .
3. $B$ is a subset of $U$ with elements $\{q, s, y, z\}$ .
4. $C$ is a subset of $U$ with elements $\{v, w, x, y, z\}$ , but it is not used in this problem.
5. $A'$ represents the complement of set $A$ with respect to the universal set $U$ .
6. We need to find the union of $A'$ and $B$ .

STEP 2

First, we need to find the complement of set $A$ , denoted as $A'$ , which consists of all elements in the universal set $U$ that are not in $A$ .
$A' = U - A$

STEP 3

List the elements of the universal set $U$ that are not in set $A$ to find $A'$ .
$A' = \{r, t, v, x, z\}$

STEP 4

Now, we need to find the union of $A'$ and $B$ , denoted as $A' \cup B$ .
$A' \cup B = A' + B - (A' \cap B)$

STEP 5

List the elements of $A'$ and $B$ .
$A' = \{r, t, v, x, z\}$ $B = \{q, s, y, z\}$

STEP 6

Combine the elements of $A'$ and $B$ to find $A' \cup B$ . Note that the element $z$ is in both $A'$ and $B$ , so it should only be listed once in the union.
$A' \cup B = \{r, t, v, x, z, q, s, y\}$

STEP 7

List the elements of $A' \cup B$ in order, as they are usually presented in set notation.
$A' \cup B = \{q, r, s, t, v, x, y, z\}$
The elements in the set $A' \cup B$ are $\{q, r, s, t, v, x, y, z\}$ .

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List the elements in the set $A^{\prime} \cup B$ , where $A = \{q, s, u, w, y\}$ and $B = \{q, s, y, z\}$ .

STEP 1

STEP 2

First, we need to find the complement of set $A$ , denoted as $A'$ , which consists of all elements in the universal set $U$ that are not in $A$ .
$A' = U - A$

STEP 3

List the elements of the universal set $U$ that are not in set $A$ to find $A'$ .
$A' = \{r, t, v, x, z\}$

STEP 4

Now, we need to find the union of $A'$ and $B$ , denoted as $A' \cup B$ .
$A' \cup B = A' + B - (A' \cap B)$

STEP 5

List the elements of $A'$ and $B$ .
$A' = \{r, t, v, x, z\}$ $B = \{q, s, y, z\}$

STEP 6

Combine the elements of $A'$ and $B$ to find $A' \cup B$ . Note that the element $z$ is in both $A'$ and $B$ , so it should only be listed once in the union.
$A' \cup B = \{r, t, v, x, z, q, s, y\}$

STEP 7

List the elements of $A' \cup B$ in order, as they are usually presented in set notation.
$A' \cup B = \{q, r, s, t, v, x, y, z\}$
The elements in the set $A' \cup B$ are $\{q, r, s, t, v, x, y, z\}$ .

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List the elements in the set A′∪BA^{\prime} \cup BA′∪B, where A={q,s,u,w,y}A = \{q, s, u, w, y\}A={q,s,u,w,y} and B={q,s,y,z}B = \{q, s, y, z\}B={q,s,y,z}.

STEP 1

STEP 2

First, we need to find the complement of set AAA, denoted as A′A'A′, which consists of all elements in the universal set UUU that are not in AAA.A′=U−AA' = U - AA′=U−A

STEP 3

List the elements of the universal set UUU that are not in set AAA to find A′A'A′.A′={r,t,v,x,z}A' = \{r, t, v, x, z\}A′={r,t,v,x,z}

STEP 4

Now, we need to find the union of A′A'A′ and BBB, denoted as A′∪BA' \cup BA′∪B.A′∪B=A′+B−(A′∩B)A' \cup B = A' + B - (A' \cap B)A′∪B=A′+B−(A′∩B)

STEP 5

List the elements of A′A'A′ and BBB.A′={r,t,v,x,z}A' = \{r, t, v, x, z\}A′={r,t,v,x,z} B={q,s,y,z}B = \{q, s, y, z\}B={q,s,y,z}

STEP 6

Combine the elements of A′A'A′ and BBB to find A′∪BA' \cup BA′∪B. Note that the element zzz is in both A′A'A′ and BBB, so it should only be listed once in the union.A′∪B={r,t,v,x,z,q,s,y}A' \cup B = \{r, t, v, x, z, q, s, y\}A′∪B={r,t,v,x,z,q,s,y}

STEP 7

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List the elements in the set $A^{\prime} \cup B$ , where $A = \{q, s, u, w, y\}$ and $B = \{q, s, y, z\}$ .

First, we need to find the complement of set $A$ , denoted as $A'$ , which consists of all elements in the universal set $U$ that are not in $A$ .
$A' = U - A$

List the elements of the universal set $U$ that are not in set $A$ to find $A'$ .
$A' = \{r, t, v, x, z\}$

Now, we need to find the union of $A'$ and $B$ , denoted as $A' \cup B$ .
$A' \cup B = A' + B - (A' \cap B)$

List the elements of $A'$ and $B$ .
$A' = \{r, t, v, x, z\}$ $B = \{q, s, y, z\}$

Combine the elements of $A'$ and $B$ to find $A' \cup B$ . Note that the element $z$ is in both $A'$ and $B$ , so it should only be listed once in the union.
$A' \cup B = \{r, t, v, x, z, q, s, y\}$