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)′={7,9,11,13,17,19}\left(E\cup F\cup G\$$right)^{\prime}$$=\left\lbrace7,9,11,13,17,19\right\rbrace

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

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

(E∪F∪G)′={7,9,11,13,15,17,19}\left(E\cup F\cup G\$$right)^{\prime}$$=\left\lbrace7,9,11,13,15,17,19\right\rbrace

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.(B) (E∪F)∩(F∪G)\left(E\cup F\right)\cap\left(F\cup G\right)

(E∪F)∩(F∪G)={2,4,5,10,15,20}\left(E\cup F\right)\cap\left(F\cup G\right)=\left\lbrace2,4,5,10,15,20\right\rbrace

(E∪F)∩(F∪G)={1,2,3,4,5,10,15,20}\left(E\cup F\right)\cap\left(F\cup G\right)=\left\lbrace1,2,3,4,5,10,15,20\right\rbrace

(E∪F)∩(F∪G)={5,10,15,20}\left(E\cup F\right)\cap\left(F\cup G\right)=\left\lbrace5,10,15,20\right\rbrace

(E∪F)∩(F∪G)={1,2,3,4,5,6,8,10,15,20}\left(E\cup F\right)\cap\left(F\cup G\right)=\left\lbrace1,2,3,4,5,6,8,10,15,20\right\rbrace

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.(C) F′∩(E∪G′$$)F^{\prime}$$\cap\left(E\cup $$G^{\prime}$$\right)

F′∩(E∪G′)={2,4,6,7,8,9,11,12,13,14,16,17,18,19}$$F^{\prime}$$\cap\left(E\cup $$G^{\prime}$$\right)=\left\lbrace2,4,6,7,8,9,11,12,13,14,16,17,18,19\right\rbrace

F′∩(E∪G′)={5,10,15,20}$$F^{\prime}$$\cap\left(E\cup $$G^{\prime}$$\right)=\left\lbrace5,10,15,20\right\rbrace

F′∩(E∪G′)={2,4,6,7,8,9,11,12,13,14,15,16,17,18,19}$$F^{\prime}$$\cap\left(E\cup $$G^{\prime}$$\right)=\left\lbrace2,4,6,7,8,9,11,12,13,14,15,16,17,18,19\right\rbrace

F′∩(E∪G′)={15,20}$$F^{\prime}$$\cap\left(E\cup $$G^{\prime}$$\right)=\left\lbrace15,20\right\rbrace

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.(D) (E∩F′)∪(G′∩F′)\left(E\cap $$F^{\prime}$$\right)\cup\$$left(G^{\prime}$$\cap $$F^{\prime}$$\right)

(E∩F′)∪(G′∩F′)={2,4,6,7,8,9,11,12,13,14,16,17,18,19}\left(E\cap $$F^{\prime}$$\right)\cup\$$left(G^{\prime}$$\cap $$F^{\prime}$$\right)=\left\lbrace2,4,6,7,8,9,11,12,13,14,16,17,18,19\right\rbrace

(E∩F′)∪(G′∩F′)={5,10,15,20}\left(E\cap $$F^{\prime}$$\right)\cup\$$left(G^{\prime}$$\cap $$F^{\prime}$$\right)=\left\lbrace5,10,15,20\right\rbrace

(E∩F′)∪(G′∩F′)={2,4,6,7,8,9,11,12,13,14,15,16,17,18,19}\left(E\cap $$F^{\prime}$$\right)\cup\$$left(G^{\prime}$$\cap $$F^{\prime}$$\right)=\left\lbrace2,4,6,7,8,9,11,12,13,14,15,16,17,18,19\right\rbrace

(E∩F′)∪(G′∩F′)={15,20}\left(E\cap $$F^{\prime}$$\right)\cup\$$left(G^{\prime}$$\cap $$F^{\prime}$$\right)=\left\lbrace15,20\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

0

Problem

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

A

$open paren E union F union G close paren prime equals open paren 1 comma 3 comma 5 comma 7 comma 9 comma 11 comma 13 comma 15 comma 17 comma 19 close paren$

B

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

C

$open paren E union F union G close paren prime equals open paren 1 comma 3 comma 7 comma 9 comma 11 comma 13 comma 17 comma 19 close paren$

D

${(E \cup F \cup G)}^{'} = {7, 9, 11, 13, 15, 17, 19}$

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) $(E \cup F) \cap (F \cup G)$

A

$(E \cup F) \cap (F \cup G) = {2, 4, 5, 10, 15, 20}$

B

$(E \cup F) \cap (F \cup G) = {1, 2, 3, 4, 5, 10, 15, 20}$

C

$(E \cup F) \cap (F \cup G) = {5, 10, 15, 20}$

D

$(E \cup F) \cap (F \cup G) = {1, 2, 3, 4, 5, 6, 8, 10, 15, 20}$

0

Problem

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

A

$F^{'} \cap (E \cup G^{'}) = {5, 10, 15, 20}$

B

$F^{'} \cap (E \cup G^{'}) = {2, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}$

C

$F^{'} \cap (E \cup G^{'}) = {15, 20}$

D

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

0

Problem

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

A

$(E \cap F^{'}) \cup (G^{'} \cap F^{'}) = {5, 10, 15, 20}$

B

$(E \cap F^{'}) \cup (G^{'} \cap F^{'}) = {2, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}$

C

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

D

$(E \cap F^{'}) \cup (G^{'} \cap F^{'}) = {15, 20}$

0

Problem

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(A) ${(A \cup B \cup C)}^{'}$

A

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

B

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

C

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

D

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

0

Problem

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(B) $A^{'} \cap B^{'} \cap C^{'}$

A

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

0

Problem

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$

A

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

B

$\left\)(A$\cup$ B$\cup$ C$\right$)^{$\prime$}=$\left\[\lbrace$9\(\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$2,3,4,5,8\(\right\]\rbrace$

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) ${(E \cup F \cup G)}^{'}$

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) $(E \cup F) \cap (F \cup G)$

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) $F^{'} \cap (E \cup G^{'})$

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) $(E \cap F^{'}) \cup (G^{'} \cap F^{'})$

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(A) ${(A \cup B \cup C)}^{'}$

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(B) $A^{'} \cap B^{'} \cap C^{'}$

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$

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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 Liberal Arts Math tutors

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(A) ${(A \cup B \cup C)}^{'}$

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(B) $A^{'} \cap B^{'} \cap C^{'}$

Use the Venn diagram to find each of the following.
$Venn diagram with three overlapping sets labeled A, B, and C, showing numbers in each region within a universal set.$
(C) $(A \cap B) \cup (B \cap C) \cup (C \cap A)$