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    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?
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    (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.
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    (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?
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    (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,
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    (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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