- #1
SpatialVacancy
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Help me construct a proof!
Consider the following set property: For all sets [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex], [tex](A-B) \cup (B-C) = (A \cup B) - (B \cap C)[/tex].
a) Use an element argument to derive this property.
b) Use an algebraic argument to derive this property.
Ok, for part (a), I know that I need to show that:
[tex](A-B) \cup (B-C) \subseteq (A \cup B) - (B \cap C)[/tex], and
[tex](A \cup B) - (B \cap C) \subseteq (A-B) \cup (B-C)[/tex] (right?).
To do this, i need to show that [tex]\forall x[/tex], if [tex]x \ \epsilon \ (A-B) \cup (B-C)[/tex], and [tex]x \ \epsilon \ (A \cup B) - (B \cap C)[/tex]. From here I do not know where to go.
For part (b), any help you can give me I would appreciate. I have written several pages of calculations and have yet to come up with anything.
Please help! This assignment is due 2/25 at 1:30 EST.
Thanks
Consider the following set property: For all sets [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex], [tex](A-B) \cup (B-C) = (A \cup B) - (B \cap C)[/tex].
a) Use an element argument to derive this property.
b) Use an algebraic argument to derive this property.
Ok, for part (a), I know that I need to show that:
[tex](A-B) \cup (B-C) \subseteq (A \cup B) - (B \cap C)[/tex], and
[tex](A \cup B) - (B \cap C) \subseteq (A-B) \cup (B-C)[/tex] (right?).
To do this, i need to show that [tex]\forall x[/tex], if [tex]x \ \epsilon \ (A-B) \cup (B-C)[/tex], and [tex]x \ \epsilon \ (A \cup B) - (B \cap C)[/tex]. From here I do not know where to go.
For part (b), any help you can give me I would appreciate. I have written several pages of calculations and have yet to come up with anything.
Please help! This assignment is due 2/25 at 1:30 EST.
Thanks