Question

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Answer 1

does a picture help?

Answer 2

The square is the universe?

Answer 3

B ∩ D = ∅ ⇒ A ∩ C = ∅. this is the part i'm confused about. How do you show a proof for this?

Answer 4

Without a Venn Diagram that is.

Answer 5

@satellite73

Answer 6

lets pick \(x\in A\) and show that \(x\) is not in \(C\)

Answer 7

okay

Answer 8

since \(x\in A\) we know \(x\in B\) as \(A\subset B\)

Answer 9

therefore, since \(B\cap D=\emptyset\) we know \(x\notin D\)

Answer 10

and since \(x\notin D\) we know \(x\notin C\) since \(C\subset D\)

Answer 11

therefore, if \(x\in A\) we know \(x\notin C\) making \(A\cap C=\emptyset\)

Answer 12

Ohhh

Answer 13

Should we always prove by choosing an element of a set and see how it relates to others?