Write the specified set using the roster method givenU={1,2,3,…,20},E={2,4,6,…,20},F={5,10,15,20},G={1,2,3,4,5}U=\left\lbrace1,2,3,\ldots,20\right\rbrace,E=\left\lbrace2,4,6,\ldots,20\right\rbrace,F=\left\lbrace5,10,15,20\right\rbrace,G=\left\lbrace1,2,3,4,5\right\rbrace.(A) (E∪F∪G)′\left(E\cup F\cup G\$$right)^{\prime}(E$$∪F∪G)′

(E∪F∪G)′={1,3,7,9,11,13,17,19}\left(E\cup F\cup G\$$right)^{\prime}$$=\left\lbrace1,3,7,9,11,13,17,19\right\rbrace

Venn Diagrams and Operations with Three Sets Explained: Definition, Examples, Practice & Video Lessons

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Concept

Venn Diagrams and Operations with Three Sets

Video duration:

5m

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Example

Venn Diagrams and Operations with Three Sets Example 1

Video duration:

4m

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Problem

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(A) $$\left$(E$\cup$ F$\cup$ G$\right$)^{$\prime$}$

A

$$\left$(E$\cup$ F$\cup$ G$\right$)^{$\prime$}=$\left$(1,3,5,7,9,11,13,15,17,19$\right$)$

B

$\left\)(E$\cup$ F$\cup$ G$\right$)^{$\prime$}=$\left\[\lbrace$7,9,11,13,17,19\(\right\]\rbrace$

C

${(E \cup F \cup G)}^{'} = {1, 3, 7, 9, 11, 13, 17, 19}$

D

$\left\)(E$\cup$ F$\cup$ G$\right$)^{$\prime$}=$\left\[\lbrace$7,9,11,13,15,17,19\(\right\]\rbrace$

0

Problem

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(B) $$\left$(E$\cup$ F$\right$)$\cap\]\left$(F$\cup$ G$\right$)$

A

$\left\)(E$\cup$ F$\right$)$\cap\]\left$(F$\cup$ G$\right$)=$\left\[\lbrace$2,4,5,10,15,20\(\right\]\rbrace$

B

$\left\)(E$\cup$ F$\right$)$\cap\]\left$(F$\cup$ G$\right$)=$\left\[\lbrace$1,2,3,4,5,10,15,20\(\right\]\rbrace$

C

$\left\)(E$\cup$ F$\right$)$\cap\]\left$(F$\cup$ G$\right$)=$\left\[\lbrace$5,10,15,20\(\right\]\rbrace$

D

$\left\)(E$\cup$ F$\right$)$\cap\]\left$(F$\cup$ G$\right$)=$\left\[\lbrace$1,2,3,4,5,6,8,10,15,20\(\right\]\rbrace$

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Problem

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(C) $F^{$\prime$}$\cap\]\left$(E$\cup$ G^{$\prime$}$\right$)$

A

$F^{$\prime$}$\cap\]\left$(E$\cup$ G^{$\prime$}$\right$)=$\left\[\lbrace$5,10,15,20$\right\]\rbrace$$

B

$F^{$\prime$}$\cap\]\left$(E$\cup$ G^{$\prime$}$\right$)=$\left\[\lbrace$2,4,6,7,8,9,11,12,13,14,15,16,17,18,19$\right\]\rbrace$$

C

$F^{$\prime$}$\cap\]\left$(E$\cup$ G^{$\prime$}$\right$)=$\left\[\lbrace$15,20$\right\]\rbrace$$

D

$F^{'} \cap (E \cup G^{'}) = {2, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19}$

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Problem

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(D) $$\left$(E$\cap$ F^{$\prime$}$\right$)$\cup\]\left$(G^{$\prime$}$\cap$ F^{$\prime$}$\right$)$ .

A

$\left\)(E$\cap$ F^{$\prime$}$\right$)$\cup\]\left$(G^{$\prime$}$\cap$ F^{$\prime$}$\right$)=$\left\[\lbrace$5,10,15,20\(\right\]\rbrace$

B

$\left\)(E$\cap$ F^{$\prime$}$\right$)$\cup\]\left$(G^{$\prime$}$\cap$ F^{$\prime$}$\right$)=$\left\[\lbrace$2,4,6,7,8,9,11,12,13,14,15,16,17,18,19\(\right\]\rbrace$

C

$\left\)(E$\cap$ F^{$\prime$}$\right$)$\cup\]\left$(G^{$\prime$}$\cap$ F^{$\prime$}$\right$)=$\left\[\lbrace$2,4,6,7,8,9,11,12,13,14,16,17,18,19\(\right\]\rbrace$

D

$\left\)(E$\cap$ F^{$\prime$}$\right$)$\cup\]\left$(G^{$\prime$}$\cap$ F^{$\prime$}$\right$)=$\left\[\lbrace$15,20\(\right\]\rbrace$

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Problem

Use the Venn diagram to find each of the following.

(A) ${(A \cup B \cup C)}^{'}$

A

$\left\)(A$\cup$ B$\cup$ C$\right$)^{$\prime$}=$\left\[\lbrace$9\(\right\]\rbrace$

B

$\left\)(A$\cup$ B$\cup$ C$\right$)^{$\prime$}=$\left\[\lbrace$2,3,4,5,8\(\right\]\rbrace$

C

$\left\)(A$\cup$ B$\cup$ C$\right$)^{$\prime$}=$\left\[\lbrace$0,1,6,7\(\right\]\rbrace$

D

$\left\)(A$\cup$ B$\cup$ C$\right$)^{$\prime$}=$\left\[\lbrace$0,1,6,7,9\(\right\]\rbrace$

0

Problem

Use the Venn diagram to find each of the following.

(B) $A^{'} \cap B^{'} \cap C^{'}$

A

${(A \cup B \cup C)}^{'} = {0, 1, 6, 7, 9}$

B

${(A \cup B \cup C)}^{'} = {2, 3, 4, 5, 8}$

C

${(A \cup B \cup C)}^{'} = {0, 1, 6, 7}$

D

${(A \cup B \cup C)}^{'} = {9}$

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Problem

Use the Venn diagram to find each of the following.

(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$

A

${(A \cup B \cup C)}^{'} = {0, 1, 6, 7, 9}$

B

${(A \cup B \cup C)}^{'} = {9}$

C

${(A \cup B \cup C)}^{'} = {0, 1, 6, 7}$

D

${(A \cup B \cup C)}^{'} = {2, 3, 4, 5, 8}$

Venn Diagrams and Operations with Three Sets: Videos & Practice Problems

Venn Diagrams and Operations with Three Sets

Venn Diagrams and Operations with Three Sets Example 1

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(A) $\(\left\)(E\(\cup\) F\(\cup\) G\(\right\))^{\(\prime\)}$

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(B) $\(\left\)(E\(\cup\) F\(\right\))\(\cap\]\left\)(F\(\cup\) G\(\right\))$

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(C) $F^{\(\prime\)}\(\cap\]\left\)(E\(\cup\) G^{\(\prime\)}\(\right\))$

Write the specified set using the roster method given
$U = {1, 2, 3, \dots, 20}, E = {2, 4, 6, \dots, 20}, F = {5, 10, 15, 20}, G = {1, 2, 3, 4, 5}$ .
(D) $\(\left\)(E\(\cap\) F^{\(\prime\)}\(\right\))\(\cup\]\left\)(G^{\(\prime\)}\(\cap\) F^{\(\prime\)}\(\right\))$ .

Use the Venn diagram to find each of the following.

(A) ${(A \cup B \cup C)}^{'}$

Use the Venn diagram to find each of the following.

(B) $A^{'} \cap B^{'} \cap C^{'}$

Use the Venn diagram to find each of the following.

(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$

Your Quantitative Reasoning tutors

Venn Diagrams and Operations with Three Sets: Videos & Practice Problems

Venn Diagrams and Operations with Three Sets

Venn Diagrams and Operations with Three Sets Example 1

Use the Venn diagram to find each of the following.(A) (A∪B∪C)′\(\left\)(A\(\cup\) B\(\cup\) C\(\right\))^{\(\prime\)}

Use the Venn diagram to find each of the following.(B) A′∩B′∩C′A^{\(\prime\)}\(\cap\) B^{\(\prime\)}\(\cap\) C^{\(\prime\)}

Use the Venn diagram to find each of the following.(C) (A∩B)∪(B∩C)∪(C∩A)\(\left\)(A\(\cap\) B\(\right\))\(\cup\[\left\)(B\(\cap\) C\(\right\))\(\cup\]\left\)(C\(\cap\) A\(\right\))

Your Quantitative Reasoning tutors

Use the Venn diagram to find each of the following.

(A) ${(A \cup B \cup C)}^{'}$

Use the Venn diagram to find each of the following.

(B) $A^{'} \cap B^{'} \cap C^{'}$

Use the Venn diagram to find each of the following.

(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$