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# Sets and subsets help! watch

1. Let U = {1,2,3,4,5,6,x,y,{1,2},{1,2,3},{ 1,2,3,4}} – where x,y are simply letters of the alphabet.

Then | U | = 11.

a. If A = {1,2,3,4}, then |A| = 4 and:
i. A ⊆ U
ii. A ⊂ U
iii. A ∈ U
iv. {A} ⊆ U
v. {A} ⊂ U, but vi. {A} ∉ U

what does the {A} mean for A? can someone explain this?
2. (Original post by mrincredibleme)
Let U = {1,2,3,4,5,6,x,y,{1,2},{1,2,3},{ 1,2,3,4}} – where x,y are simply letters of the alphabet.

Then | U | = 11.

a. If A = {1,2,3,4}, then |A| = 4 and:
i. A ⊆ U
ii. A ⊂ U
iii. A ∈ U
iv. {A} ⊆ U
v. {A} ⊂ U, but vi. {A} ∉ U

what does the {A} mean for A? can someone explain this?
Since A = {1,2,3,4}

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

i.e. {A} is a set containing the set A.

Since {1,2,3,4} is an element of U, {{1,2,3,4}} must be a subset of U because it is a set containing one of the elements of U.

But while {{1,2,3,4}} is a subset of U, it is not one of the elements of U.
3. (Original post by notnek)
Since A = {1,2,3,4}

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

i.e. {A} is a set containing the set A.

Since {1,2,3,4} is an element of U, {{1,2,3,4}} must be a subset of U because it is a set containing one of the elements of U.

But while {{1,2,3,4}} is a subset of U, it is not one of the elements of U.
why is {{1,2,3,4}} not an element of U?
4. (Original post by mrincredibleme)
why is {{1,2,3,4}} not an element of U?
Elements of U are separated by commas in U. There are 11 elements in U and {{1,2,3,4}} is not one of them.

But {1,2,3,4} is an element of U,

{{1,2,3,4}} is a set containing an element of U so it is a subset of U,
5. (Original post by notnek)
Elements of U are separated by commas in U. There are 11 elements in U and {{1,2,3,4}} is not one of them.

But {1,2,3,4} is an element of U,

{{1,2,3,4}} is a set containing an element of U so it is a subset of U,
ah thank you very much!

I've got another question!

can we map Q onto R and are they the same size?

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