For two sets A and B , prove that A intersection B ^ c = phy that implies a is a subset of b​

Question

For two sets A and B , prove that A intersection B ^ c = phy that implies a is a subset of b​

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Aaliyah 4 weeks 2021-11-02T06:54:27+00:00 1 Answer 0 views 0

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    2021-11-02T06:55:37+00:00

    hey mate your answer :

    First, assume that A ⊆B and we have to prove that A ∩B = A

    Proof: Given A ⊆B

    Let x ∈ A ∩ B which implies that x ∈ A and x ∈B. Hence we can imply that

    A ∩ B ⊆ A (We started with an element in A ∩ B and concluded that it is in A)

    ——(1)

    Now, let x ∈ A which implies x ∈B (as A ⊆B)

    Hence, x ∈ A ∩ B, which in turn implies

    A ⊆ A ∩ B ——-(2)

    From (1) and (2), A ∩B = A

    Conversely, assume A ∩B = A and we have to prove that A ⊆B

    Proof: Given A ∩B = A

    Let x ∈ A , then since A ∩B = A , x ∈ A ∩ B

    This implies x ∈B, hence in turn implies A ⊆B (We have an element in A and we proved that it is in B).

    I hope it’s helped you please make me a brainlist and follow me also

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