Questions: Assignment: 5.5 Sets Score: 3 / 8 Answered: 3 / 8 Question 4 Let S be the universal set, where: S=1,2,3, ..., 18,19,20 Let sets A and B be subsets of S, where: Set A=2,5,6,8,10,12,13,16,19,20 Set B=1,2,5,7,9,10,12,14,15,16,19,20 Find the following: LIST the elements in the set ( A ∩ Bc ): (A ∩ Bc)= Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( B ∩ Ac ): (B ∩ Ac)= Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.

Assignment: 5.5 Sets
Score: 3 / 8 Answered: 3 / 8
Question 4

Let S be the universal set, where:
S=1,2,3, ..., 18,19,20

Let sets A and B be subsets of S, where:
Set A=2,5,6,8,10,12,13,16,19,20
Set B=1,2,5,7,9,10,12,14,15,16,19,20
Find the following:
LIST the elements in the set ( A ∩ Bc ):
(A ∩ Bc)=
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( B ∩ Ac ):
(B ∩ Ac)=
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.
Transcript text: Assignment: 5.5 Sets Score: $3 / 8$ Answered: $3 / 8$ Question 4 Let $S$ be the universal set, where: \[ S=\{1,2,3, \ldots, 18,19,20\} \] Let sets $A$ and $B$ be subsets of $S$, where: Set $A=\{2,5,6,8,10,12,13,16,19,20\}$ Set $B=\{1,2,5,7,9,10,12,14,15,16,19,20\}$ Find the following: LIST the elements in the set ( $A \cap B^{c}$ ): \[ \left(A \cap B^{\subseteq}\right)=\{ \] $\qquad$ \} Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( $B \cap A^{\mathrm{c}}$ ): $\left(B \cap A^{C}\right)=\{$ $\square$ Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.
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Solution

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Solution Steps

Step 1: Define the Universal Set $S$

The universal set $S$ is defined by the range from 1 to 20, inclusive. So, $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$.

Step 2: Calculate the Union of $A \cup B$

The union of $A$ and $B$, denoted as $A \cup B$, combines all unique elements from both sets. So, $A \cup B = \{1, 2, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 20\}$.

Step 3: Calculate the Intersection of $A \cap B$

The intersection of $A$ and $B$, denoted as $A \cap B$, lists all elements present in both sets. So, $A \cap B = \{2, 5, 10, 12, 16, 19, 20\}$.

Step 4: Calculate the Complements $A^c$, $B^c$, and $C^c$

The complement of $A$ within the universal set $S$, denoted as $A^c$, lists all elements of $S$ not in $A$. So, $A^c = \{1, 3, 4, 7, 9, 11, 14, 15, 17, 18\}$. The complement of $B$ within the universal set $S$, denoted as $B^c$, lists all elements of $S$ not in $B$. So, $B^c = \{3, 4, 6, 8, 11, 13, 17, 18\}$. No set $C$ was provided, so $C^c$ is not applicable.

Final Answer:

The union $A \cup B = \{1, 2, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 20\}$, the intersection $A \cap B = \{2, 5, 10, 12, 16, 19, 20\}$, the complement $A^c = \{1, 3, 4, 7, 9, 11, 14, 15, 17, 18\}$, and $B^c = \{3, 4, 6, 8, 11, 13, 17, 18\}$.

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