Find the complement of each set. U={11,12,13,14,15,16}U=\left\lbrace{11,12,13,14,15,16}\right\rbraceA={12,15,16}A=\left\lbrace{12,15,16}\right\rbrace

A′={11,13,14}$$A^{\prime}$$=\left\lbrace11,13,14\right\rbrace

A′={12,15,16}$$A^{\prime}$$=\left\lbrace12,15,16\right\rbrace

A′={11,12,13,14}$$A^{\prime}$${=\left\lbrace11,12,13,14\right\rbrace}

A′={11,13,14,15}$$A^{\prime}$$=\left\lbrace{11,13,14,15}\right\rbrace

Find the complement of each set.U={u,v,w,x,y,z}U=\left\lbrace{u,v,w,x,y,z}\right\rbraceA={v,x,z}A={\left\lbrace v,x,z\right\rbrace}

A′={u,w,y}$$A^{\prime}$$=\left\lbrace u,w,y\right\rbrace

A′={v,x,z}$$A^{\prime}$$=\left\lbrace v,x,z\right\rbrace

A′={u,v,w,y}$$A^{\prime}$$=\left\lbrace u,v,w,y\right\rbrace

A′={u,w,x,y}$$A^{\prime}$$=\left\lbrace u,w,x,y\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}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}E′$$E^{\prime}$$

E′={1,3,5,7,9,11,13,15,17,19}$$E^{\prime}$$=\left\lbrace1,3,5,7,9,11,13,15,17,19\right\rbrace

E′={2,4,6,8,10,12,14,16,18,20}$$E^{\prime}$$=\left\lbrace2,4,6,8,10,12,14,16,18,20\right\rbrace

E′={1,2,3,5,7,9,11,13,15,17,19}$$E^{\prime}$$=\left\lbrace1,2,3,5,7,9,11,13,15,17,19\right\rbrace

E′={1,3,5,7,9,15,20}$$E^{\prime}$$=\left\lbrace1,3,5,7,9,15,20\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}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}F′$$F^{\prime}$$

F′={1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19}$$F^{\prime}$$=\left\lbrace1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19\right\rbrace

F′={1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,20}$$F^{\prime}$$=\left\lbrace1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,20\right\rbrace

F′={1,2,3,4,6,7,8,9,11,12,13,14,15,16,17,18,19}$$F^{\prime}$$=\left\lbrace1,2,3,4,6,7,8,9,11,12,13,14,15,16,17,18,19\right\rbrace

F′={1,2,3,4,6,7,8,9,10,11,12,13,14,16,17,18,19}$$F^{\prime}$$=\left\lbrace1,2,3,4,6,7,8,9,10,11,12,13,14,16,17,18,19\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}U=\left\lbrace{1,2,3,\ldots,20}\right\rbrace,E={\left\lbrace2,4,6,\ldots,20\right\rbrace},F={\left\lbrace5,10,15,20\right\rbrace}U′$$U^{\prime}$$

U′={}$$U^{\prime}$$=\left\lbrace\right\rbrace

U′={1,2,3,…,20}$$U^{\prime}$$=\left\lbrace1,2,3,\ldots,20\right\rbrace

U′={21,22,23,…}$$U^{\prime}$$=\left\lbrace21,22,23,\ldots\right\rbrace

U′={5,10,15,20}$$U^{\prime}$$=\left\lbrace5,10,15,20\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}U=\left\lbrace{1,2,3,\ldots,20}\right\rbrace,E={\left\lbrace2,4,6,\ldots,20\right\rbrace},F={\left\lbrace5,10,15,20\right\rbrace}∅′∅'

∅′={1,2,3,…,20}\$$emptyset^{\prime}$$=\left\lbrace{1,2,3,\ldots,20}\right\rbrace

∅′={}\$$emptyset^{\prime}$$=\left\lbrace{}\right\rbrace

∅′={2,4,6,…8,20}\$$emptyset^{\prime}$$=\left\lbrace{}2,4,6,\ldots8,20\right\rbrace

∅′={1,3,5,7,9,11,13,15,17,19}\$$emptyset^{\prime}$$=\left\lbrace{}1,3,5,7,9,11,13,15,17,19\right\rbrace

Label the Venn diagram with the elements that belong in each set using U={0,1,2,…,9}U={\left\lbrace0,1,2,\ldots,9\right\rbrace},E={0,2,4,6,8}E={\left\lbrace0,2,4,6,8\right\rbrace}. Then find & shade O=E’.

O={1,3,5,7,9}O=\left\lbrace1,3,5,7,9\right\rbraceO={1,3,5,7,9}

O={1,3,5,7,9}O=\left\lbrace1,3,5,7,9\right\rbrace

O={0,2,4,6,8}O=\left\lbrace0,2,4,6,8\right\rbraceO={0,2,4,6,8}

O={0,2,4,6,8}O=\left\lbrace0,2,4,6,8\right\rbrace

Complement of a Set Explained: Definition, Examples, Practice & Video Lessons

0

Concept

Complement of a Set

Video duration:

5m

0

Problem

Find the complement of each set.
$U = {11, 12, 13, 14, 15, 16}$
$A = {12, 15, 16}$

A

$A^{'} = {12, 15, 16}$

B

$A^{'} = {11, 12, 13, 14}$

C

$A^{'} = {11, 13, 14}$

D

$A^{'} = {11, 13, 14, 15}$

0

Problem

Find the complement of each set.
$U = {u, v, w, x, y, z}$
$A = {v, x, z}$

A

$A^{'} = {v, x, z}$

B

$A^{'} = {u, w, y}$

C

$A^{'} = {u, v, w, y}$

D

$A^{'} = {u, w, x, y}$

0

Problem

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

A

$E^{'} = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}$

B

$E^{'} = {1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19}$

C

$E^{'} = {1, 3, 5, 7, 9, 15, 20}$

D

$E^{'} = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}$

0

Problem

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

A

$F^{'} = {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20}$

B

$F^{'} = {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19}$

C

$F^{'} = {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19}$

D

$F^{'} = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19}$

0

Problem

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

A

$U^{'} = {1, 2, 3, \dots, 20}$

B

$U^{'} = {}$

C

$U^{'} = {21, 22, 23, \dots}$

D

$U^{'} = {5, 10, 15, 20}$

0

Problem

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

A

$\emptyset^{'} = {1, 2, 3, \dots, 20}$

B

$\emptyset^{'} = {}$

C

$\emptyset^{'} = {2, 4, 6, \dots 8, 20}$

D

$\emptyset^{'} = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}$

0

Problem

Shade the set B=A’ on the Venn diagram. Then write sets A,B, & U using the roster method.
$Venn diagram with circle A containing numbers 1, 2, 3, 4, 5 inside a rectangle U with numbers 0, 6, 7, 8, 9 outside.$

A

$Venn diagram with circle A shaded containing numbers 1,2,3,4,5; outside are 0,6,7,8,9 in the universal set.$

$A=$\left\[\lbrace$1,2,3,4,5$\right\]\rbrace$$

$B=$\left\[\lbrace$0,6,7,8,9$\right\]\rbrace$$

$U=$\left\[\lbrace$0,1,2,3,4,5,6,7,8,9$\right\]\rbrace$$

B

$Venn diagram with circle A shaded containing numbers 1,2,3,4,5; outside are 0,6,7,8,9 in the universal set.$

$A=$\left\[\lbrace$1,2,3,4,5$\right\]\rbrace$$

$B = {}$

$U=$\left\[\lbrace$0,1,2,3,4,5,6,7,8,9$\right\]\rbrace$$

C

$Venn diagram with universal set numbers 0-9, highlighting the complement of set A as set B outside the circle.$

$A=$\left\[\lbrace$1,2,3,4,5$\right\]\rbrace$$

$B=$\left\]\lbrace\[\right\]\rbrace$$

$U=$\left\[\lbrace$0,1,2,3,4,5,6,7,8,9$\right\]\rbrace$$

D

$Venn diagram with universal set numbers 0-9, highlighting the complement of set A as set B outside the circle.$

$A = {1, 2, 3, 4, 5}$

$B = {0, 6, 7, 8, 9}$

$U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$

0

Problem

Label the Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}$ ,
$E = {0, 2, 4, 6, 8}$ . Then find & shade O=E’.
$Rectangle labeled U with circle E inside; U contains numbers 0 to 9, E contains even numbers, O is complement of E.$

A

$Venn diagram with universal set U containing 0-9, circle E with even numbers 0,2,4,6,8, and outside numbers 1,3,5,7,9 shaded.$

$O=$\left\[\lbrace$1,3,5,7,9$\right\]\rbrace$$

B

$Venn diagram with universal set U containing numbers 0-9, set E with even numbers shaded inside the circle.$

$O = {1, 3, 5, 7, 9}$

C

$Venn diagram with universal set U containing 0-9, circle E with even numbers 0,2,4,6,8, and outside numbers 1,3,5,7,9 shaded.$

$O=$\left\[\lbrace$0,2,4,6,8$\right\]\rbrace$$

D

$Venn diagram with universal set U containing numbers 0-9, set E with even numbers shaded inside the circle.$

$O = {0, 2, 4, 6, 8}$

Complement of a Set: Videos & Practice Problems

Complement of a Set

Find the complement of each set.
$U = {11, 12, 13, 14, 15, 16}$
$A = {12, 15, 16}$

Find the complement of each set.
$U = {u, v, w, x, y, z}$
$A = {v, x, z}$

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

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

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

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

Shade the set B=A’ on the Venn diagram. Then write sets A,B, & U using the roster method.
$Venn diagram with circle A containing numbers 1, 2, 3, 4, 5 inside a rectangle U with numbers 0, 6, 7, 8, 9 outside.$

Label the Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}$ ,
$E = {0, 2, 4, 6, 8}$ . Then find & shade O=E’.
$Rectangle labeled U with circle E inside; U contains numbers 0 to 9, E contains even numbers, O is complement of E.$

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Complement of a Set: Videos & Practice Problems

Complement of a Set

Find the complement of each set. U={11,12,13,14,15,16}U=\(\left\]\lbrace{11,12,13,14,15,16}\[\right\]\rbrace\)A={12,15,16}A=\(\left\]\lbrace{12,15,16}\[\right\]\rbrace\)

Find the complement of each set.U={u,v,w,x,y,z}U=\(\left\]\lbrace{u,v,w,x,y,z}\[\right\]\rbrace\)A={v,x,z}A={\(\left\[\lbrace\) v,x,z\(\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}U={\(\left\[\lbrace\)1,2,3,\(\ldots\),20\(\right\]\rbrace\)},E={\(\left\[\lbrace\)2,4,6,\(\ldots\),20\(\right\]\rbrace\)},F={\(\left\[\lbrace\)5,10,15,20\(\right\]\rbrace\)}E′E^{\(\prime\)}

Write the specified set using the roster method givenU={1,2,3,…,20},E={2,4,6,…,20},F={5,10,15,20}U={\(\left\[\lbrace\)1,2,3,\(\ldots\),20\(\right\]\rbrace\)},E={\(\left\[\lbrace\)2,4,6,\(\ldots\),20\(\right\]\rbrace\)},F={\(\left\[\lbrace\)5,10,15,20\(\right\]\rbrace\)}F′F^{\(\prime\)}

Write the specified set using the roster method givenU={1,2,3,…,20},E={2,4,6,…,20},F={5,10,15,20}U=\(\left\]\lbrace{1,2,3,\ldots,20}\[\right\]\rbrace\),E={\(\left\[\lbrace\)2,4,6,\(\ldots\),20\(\right\]\rbrace\)},F={\(\left\[\lbrace\)5,10,15,20\(\right\]\rbrace\)}U′U^{\(\prime\)}

Write the specified set using the roster method givenU={1,2,3,…,20},E={2,4,6,…,20},F={5,10,15,20}U=\(\left\]\lbrace{1,2,3,\ldots,20}\[\right\]\rbrace\),E={\(\left\[\lbrace\)2,4,6,\(\ldots\),20\(\right\]\rbrace\)},F={\(\left\[\lbrace\)5,10,15,20\(\right\]\rbrace\)}∅′∅'

Shade the set B=A’ on the Venn diagram. Then write sets A,B, & U using the roster method.

Label the Venn diagram with the elements that belong in each set using U={0,1,2,…,9}U={\(\left\[\lbrace\)0,1,2,\(\ldots\),9\(\right\]\rbrace\)},E={0,2,4,6,8}E={\(\left\[\lbrace\)0,2,4,6,8\(\right\]\rbrace\)}. Then find & shade O=E’.

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Find the complement of each set.
$U = {11, 12, 13, 14, 15, 16}$
$A = {12, 15, 16}$

Find the complement of each set.
$U = {u, v, w, x, y, z}$
$A = {v, x, z}$

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

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

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

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

Shade the set B=A’ on the Venn diagram. Then write sets A,B, & U using the roster method.
$Venn diagram with circle A containing numbers 1, 2, 3, 4, 5 inside a rectangle U with numbers 0, 6, 7, 8, 9 outside.$

Label the Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}$ ,
$E = {0, 2, 4, 6, 8}$ . Then find & shade O=E’.
$Rectangle labeled U with circle E inside; U contains numbers 0 to 9, E contains even numbers, O is complement of E.$