Subsets: Videos & Practice Problems

True

False; $\{2,4\}\subset \left\{1,2,3,4,5\right\}$

False; $\{2,4\}⊈\left\{1,2,3,4,5\right\}$

Cannot be determined.

True

False; $\{a,b,c\}\subset \{a,c,d\}$

False; $\{a,b,c\}⊈\{a,c,d\}$

Cannot be determined.

True

False; $\left\{3,6,9\right\}\subset \{3,6,9,12,18\}$

False; $\left\{3,6,9\right\}\subseteq \{3,6,9,12,18\}$

Cannot be determined

True

False; $\{p,q,r,s\}\subset \{p,q,t,u\}$

False; $\{p,q,r,s\}\subseteq \{p,q,t,u\}$

Cannot be determined

Subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\}$; Proper subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\}$

Subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\},\{red,blue\}$; Proper subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\}$

Subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\}$; Proper subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\},\{red,blue\}$ $\varnothing ,\left\{red\right\},\left\{blue\right\}$

Subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\},\{red,blue\}$; Proper subsets: $\varnothing ,\left\{red\right\},\left\{blue\right\},\{red,blue\}$

Subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\},\{apple,banana,orange\}$

Proper subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\}$

Subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\}$

Proper subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\},\{apple,banana,orange\}$

Subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\}$

Proper subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\}$

Subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\},\{apple,banana,orange\}$

Proper subsets: $\varnothing ,\left\{apple\right\},\left\{banana\right\},\left\{orange\right\},\{apple,banana\},\{apple,orange\},\{banana,orange\},\{apple,banana,orange\}$

Subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,8,11\(\right\]\rbrace\)$

Proper subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\)$

Subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\)$

Proper subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,8,11\(\right\]\rbrace\)$

Subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,8,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8,11\(\right\]\rbrace\)$

Proper subsets: $\(\emptyset\),\(\left\[\lbrace\)2\(\right\]\rbrace\),\(\left\[\lbrace\)5\(\right\]\rbrace\),\(\left\[\lbrace\)8\(\right\]\rbrace\),\(\left\[\lbrace\)11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5\(\right\]\rbrace\),\(\left\[\lbrace\)2,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8\(\right\]\rbrace\),\(\left\[\lbrace\)5,11\(\right\]\rbrace\),\(\left\[\lbrace\)8,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,8\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,8,11\(\right\]\rbrace\),\(\left\[\lbrace\)5,8,11\(\right\]\rbrace\),\(\left\[\lbrace\)2,5,8,11\(\right\]\rbrace\)$

Subsets: $\varnothing ,\left\{2\right\},\left\{5\right\},\left\{8\right\},\left\{11\right\},\{2,5\},\{2,8\},\{2,11\},\{5,8\},\{5,11\},\{8,11\},\{2,5,8\},\{2,5,11\},\{2,8,11\},\{5,8,11\},\{2,5,8,11\}$

Proper subsets: $\varnothing ,\left\{2\right\},\left\{5\right\},\left\{8\right\},\left\{11\right\},\{2,5\},\{2,8\},\{2,11\},\{5,8\},\{5,11\},\{8,11\},\{2,5,8\},\{2,5,11\},\{2,8,11\},\{5,8,11\}$