A U ∅ = A

Discussion in 'Calculator Requests' started by math_celebrity, Sep 27, 2021.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A U ∅ = A

    Let x ∈ S, where S is the universal set.

    First we show that if A ∪ Ø ⊂ A.

    Let x ∈ A ∪ Ø.

    Then x ∈ A or x ∈ Ø. by definition of the empty set, x cannot be an element in Ø.

    So by assumption, x ∈ A ∪ Ø, x must be in A.

    So A ∪ Ø ⊂ A.

    Next, we show that A ⊂ A ∪ Ø.

    This is true because the set resulting from the union of two sets contains both of the sets forms the union

    Since A ∪ Ø ⊂ A and A ⊂ A ∪ Ø, we have that A ∪ Ø = A.

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