Question

For any sets A & B prove that ∪ ( ∩ B) = A​

Answer 1

Answer:

(123l) is unoin to (123)

Answer 2

Answer:

Consider the following (I’m using ∨ for “or” and ∧ for “and”):

(A−B)∪(A∩B)={x∣x∈A∧x∉B}∪{x∣x∈A∧x∈B} (Definition of set difference, intersection)

={x∣(x∈A∧x∉B)∨(x∈A∧x∈B)} (Definition of union)

={x∣x∈A∧(x∈B∨x∉B)} (Distributivity of ∧ over ∨ )

={x∣x∈A}=A

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