Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.{3,6,9}⊈{3,6,9,12,18}\left\lbrace{3,6,9}\right\rbrace\nsubseteq{\left\lbrace3,6,9,12,18\right\rbrace}

False; {3,6,9}⊂{3,6,9,12,18}\left\lbrace{3,6,9}\right\rbrace\subset{\left\lbrace3,6,9,12,18\right\rbrace} OR {3,6,9}⊆{3,6,9,12,18}\left\lbrace{3,6,9}\right\rbrace\subseteq{\left\lbrace3,6,9,12,18\right\rbrace}

False; {3,6,9}⊂{3,6,9,12,18}\left\lbrace{3,6,9}\right\rbrace\subset{\left\lbrace3,6,9,12,18\right\rbrace}

False; {3,6,9}⊆{3,6,9,12,18}\left\lbrace{3,6,9}\right\rbrace\subseteq{\left\lbrace3,6,9,12,18\right\rbrace}

For each of the following, list all subsets & proper subsets.A={red,blue}A={\left\lbrace red,blue\right\rbrace}

Subsets: ∅,{red},{blue},{red,blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace,\left\lbrace red,blue\right\rbrace; Proper subsets: ∅,{red},{blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace

Subsets: ∅,{red},{blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace; Proper subsets: ∅,{red},{blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace

Subsets: ∅,{red},{blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace; Proper subsets: ∅,{red},{blue},{red,blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace,\left\lbrace red,blue\right\rbrace

Subsets: ∅,{red},{blue},{red,blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace,\left\lbrace red,blue\right\rbrace; Proper subsets: ∅,{red},{blue},{red,blue}\emptyset,\left\lbrace red\right\rbrace,\left\lbrace blue\right\rbrace,\left\lbrace red,blue\right\rbrace

For each of the following, list all subsets & proper subsets.B={apple,banana,orange}B={\left\lbrace apple,banana,orange\right\rbrace}.

Subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange},{apple,banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace,\left\lbrace apple,banana,orange\right\rbrace.Proper subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace

Subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbraceProper subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace

Subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbraceProper subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange},{apple,banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace,\left\lbrace apple,banana,orange\right\rbrace

Subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange},{apple,banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace,\left\lbrace apple,banana,orange\right\rbraceProper subsets: ∅,{apple},{banana},{orange},{apple,banana},{apple,orange},{banana,orange},{apple,banana,orange}\emptyset,\left\lbrace apple\right\rbrace,\left\lbrace banana\right\rbrace,\left\lbrace orange\right\rbrace,\left\lbrace apple,banana\right\rbrace,\left\lbrace apple,orange\right\rbrace,\left\lbrace banana,orange\right\rbrace,\left\lbrace apple,banana,orange\right\rbrace

For each of the following, list all subsets & proper subsets.C={2,5,8,11}C={\left\lbrace2,5,8,11\right\rbrace}

Subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8},{2,5,11},{2,8,11},{5,8,11},{2,5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8\right\rbrace,\left\lbrace2,5,11\right\rbrace,\left\lbrace2,8,11\right\rbrace,\left\lbrace5,8,11\right\rbrace,\left\lbrace2,5,8,11\right\rbraceProper subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8},{2,5,11},{2,8,11},{5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8\right\rbrace,\left\lbrace2,5,11\right\rbrace,\left\lbrace2,8,11\right\rbrace,\left\lbrace5,8,11\right\rbrace

Subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8,11\right\rbraceProper subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace

Subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbraceProper subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8,11\right\rbrace

Subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8},{2,5,11},{2,8,11},{5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8\right\rbrace,\left\lbrace2,5,11\right\rbrace,\left\lbrace2,8,11\right\rbrace,\left\lbrace5,8,11\right\rbraceProper subsets: ∅,{2},{5},{8},{11},{2,5},{2,8},{2,11},{5,8},{5,11},{8,11},{2,5,8},{2,5,11},{2,8,11},{5,8,11},{2,5,8,11}\emptyset,\left\lbrace2\right\rbrace,\left\lbrace5\right\rbrace,\left\lbrace8\right\rbrace,\left\lbrace11\right\rbrace,\left\lbrace2,5\right\rbrace,\left\lbrace2,8\right\rbrace,\left\lbrace2,11\right\rbrace,\left\lbrace5,8\right\rbrace,\left\lbrace5,11\right\rbrace,\left\lbrace8,11\right\rbrace,\left\lbrace2,5,8\right\rbrace,\left\lbrace2,5,11\right\rbrace,\left\lbrace2,8,11\right\rbrace,\left\lbrace5,8,11\right\rbrace,\left\lbrace2,5,8,11\right\rbrace

Subsets Explained: Definition, Examples, Practice & Video Lessons

0

Concept

Venn Diagrams

Video duration:

4m

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0

Problem

Label the Venn diagram with the elements that belong in each set using
$U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}$

A

$Venn diagram with universal set 0-9, set A containing 1,3,5, set B containing 6,8, and intersection with 7,9.$

B

$Venn diagram with sets A and B inside universal set U, showing elements distributed according to set membership.$

C

$Venn diagram with universal set 0-9, set A containing 1,3,5, set B containing 6,8, and intersection containing 2,4.$

D

$Venn diagram with universal set 0–9, circle A containing 1,3,5, circle B containing 6,8, and overlap containing 2,4.$

0

Example

Venn Diagrams Example 1

Subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}, {a p p l e, b a n a n a, o r a n g e}$ .

Proper subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}$

B

Subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}$

Proper subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}$

C

Subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}$

Proper subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}, {a p p l e, b a n a n a, o r a n g e}$

D

Subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}, {a p p l e, b a n a n a, o r a n g e}$

Proper subsets: $\emptyset, {a p p l e}, {b a n a n a}, {o r a n g e}, {a p p l e, b a n a n a}, {a p p l e, o r a n g e}, {b a n a n a, o r a n g e}, {a p p l e, b a n a n a, o r a n g e}$

0

Problem

For each of the following, list all subsets & proper subsets.
$C = {2, 5, 8, 11}$

A

Subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8, 11}$

Proper subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}$

B

Subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}$

Proper subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8, 11}$

C

Subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8}, {2, 5, 11}, {2, 8, 11}, {5, 8, 11}$

Proper subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8}, {2, 5, 11}, {2, 8, 11}, {5, 8, 11}, {2, 5, 8, 11}$

D

Subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8}, {2, 5, 11}, {2, 8, 11}, {5, 8, 11}, {2, 5, 8, 11}$

Proper subsets: $\emptyset, {2}, {5}, {8}, {11}, {2, 5}, {2, 8}, {2, 11}, {5, 8}, {5, 11}, {8, 11}, {2, 5, 8}, {2, 5, 11}, {2, 8, 11}, {5, 8, 11}$

0

Problem

Create a Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 3}$
Hint: B⊆A

A

$Venn diagram showing universal set 0-9 with set A containing 1-5 and subset B containing 2, 3, 4 inside A.$

B

$Venn diagram showing universal set 0-9, set A with 1-5, and subset B with 2, 3, 4 inside A.$

C

$Venn diagram showing universal set U with sets A and B inside, B fully contained within A, displaying their elements.$

D

Venn diagram showing set B inside set A, with numbers 2, 3, 4 in B; 1, 5 in A only; and 0, 6, 7, 8, 9 outside.

0

Example

Subsets Example 2

Video duration:

5m

Subsets: Videos & Practice Problems

Venn Diagrams

Label the Venn diagram with the elements that belong in each set using
$U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}$

Venn Diagrams Example 1

Subsets

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${2, 4} \subseteq {1, 2, 3, 4, 5}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${a, b, c} \subseteq {a, c, d}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${3, 6, 9} ⊈ {3, 6, 9, 12, 18}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${p, q, r, s} ⊈ {p, q, t, u}$

For each of the following, list all subsets & proper subsets.
$A = {r e d, b l u e}$

For each of the following, list all subsets & proper subsets.
$B = {a p p l e, b a n a n a, o r a n g e}$ .

For each of the following, list all subsets & proper subsets.
$C = {2, 5, 8, 11}$

Create a Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 3}$
Hint: B⊆A

Subsets Example 2

Your Quantitative Reasoning tutors

Subsets: Videos & Practice Problems

Venn Diagrams

Label the Venn diagram with the elements that belong in each set usingU={0,1,2,…,9},A={1,2,3,4,5},B={2,4,6,8}U={\(\left\[\lbrace\)0,1,2,\(\ldots\),9\(\right\]\rbrace\)},A={\(\left\[\lbrace\)1,2,3,4,5\(\right\]\rbrace\)},B={\(\left\[\lbrace\)2,4,6,8\(\right\]\rbrace\)}

Venn Diagrams Example 1

Subsets

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.{2,4}⊆{1,2,3,4,5}{\(\left\[\lbrace\)2,4\(\right\]\rbrace\)}\(\subseteq\[\left\]\lbrace{1,2,3,4,5}\[\right\]\rbrace\)

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.{a,b,c}⊆{a,c,d}{\(\left\[\lbrace\) a,b,c\(\right\]\rbrace\)}\(\subseteq{\left\lbrace a,c,d\right\rbrace}\)

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.{3,6,9}⊈{3,6,9,12,18}\(\left\[\lbrace{3,6,9}\]\right\[\rbrace\]\nsubseteq{\left\lbrace3,6,9,12,18\right\rbrace}\)

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.{p,q,r,s}⊈{p,q,t,u}{\(\left\[\lbrace\) p,q,r,s\(\right\]\rbrace\)}\(\nsubseteq{\left\lbrace p,q,t,u\right\rbrace}\)

For each of the following, list all subsets & proper subsets.A={red,blue}A={\(\left\[\lbrace\) red,blue\(\right\]\rbrace\)}

For each of the following, list all subsets & proper subsets.B={apple,banana,orange}B={\(\left\[\lbrace\) apple,banana,orange\(\right\]\rbrace\)}.

For each of the following, list all subsets & proper subsets.C={2,5,8,11}C={\(\left\[\lbrace\)2,5,8,11\(\right\]\rbrace\)}

Create a Venn diagram with the elements that belong in each set using U={0,1,2,…,9},A={1,2,3,4,5},B={2,4,3}U={\(\left\[\lbrace\)0,1,2,\(\ldots\),9\(\right\]\rbrace\)},A=\(\left\[\lbrace{1,2,3,4,5}\]\right\[\rbrace\),B=\(\left\]\lbrace{2,4,3}\[\right\]\rbrace\)Hint: B⊆A

Subsets Example 2

Your Quantitative Reasoning tutors

Label the Venn diagram with the elements that belong in each set using
$U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${2, 4} \subseteq {1, 2, 3, 4, 5}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${a, b, c} \subseteq {a, c, d}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${3, 6, 9} ⊈ {3, 6, 9, 12, 18}$

Determine if each statement is true or false. If false, make it true using one of the symbols: ⊂, ⊆, ⊈.
${p, q, r, s} ⊈ {p, q, t, u}$

For each of the following, list all subsets & proper subsets.
$A = {r e d, b l u e}$

For each of the following, list all subsets & proper subsets.
$B = {a p p l e, b a n a n a, o r a n g e}$ .

For each of the following, list all subsets & proper subsets.
$C = {2, 5, 8, 11}$

Create a Venn diagram with the elements that belong in each set using $U = {0, 1, 2, \dots, 9}, A = {1, 2, 3, 4, 5}, B = {2, 4, 3}$
Hint: B⊆A