Proof: let a,b, and c be sets. if "A ⊆ B U C" and A ∩ B = ∅, then prove A ⊆ C.
Help Please!!!
Remove B from both sides of the first statement:
(A \ B) ⊆ ((B U C) \ B)
There is nothing in B that is also in A (A ∩ B = ∅) so (A \ B) = A. Also, note that (B U C) \ B = C so the above statement reduces to:
A ⊆ C
QED
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Verified answer
Remove B from both sides of the first statement:
(A \ B) ⊆ ((B U C) \ B)
There is nothing in B that is also in A (A ∩ B = ∅) so (A \ B) = A. Also, note that (B U C) \ B = C so the above statement reduces to:
A ⊆ C
QED