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Sets and subsets help!

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?
Reply 1
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.
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?
Reply 3
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,
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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