Discrete Mathematics Help
Posted: Mon 09 Feb, 2009 12:46 am
I'm finding my math class a bit tricky and was wondering if anyone could help.
Here's my problem:
True or False: For each of the following statements, determine whether the statement is true or false and then prove your assertion. That is, for each true statement, please supply a proof, and for each false statement, present a counterexample (with explanation).
In the following, A, B, and C denote sets.
a.) A-(B-C)=(A-B)-C.
b.) (A-B)-C=(A-C)-B.
c.) (A∪B)-C=(A-C)∩(B-C).
d.) If A=B-C, then B=A∪C.
e.) If B=A∪C, then A=B-C.
f.) |A-B|=|A|-|B|.
g.) (A-B)∪B=A.
h.) (A∪B)-B=A.
Simply stating why each is true or false would be fine. Explanations always help, however.
This may become a periodical thread. Thanks for the help.
Here's my problem:
True or False: For each of the following statements, determine whether the statement is true or false and then prove your assertion. That is, for each true statement, please supply a proof, and for each false statement, present a counterexample (with explanation).
In the following, A, B, and C denote sets.
a.) A-(B-C)=(A-B)-C.
b.) (A-B)-C=(A-C)-B.
c.) (A∪B)-C=(A-C)∩(B-C).
d.) If A=B-C, then B=A∪C.
e.) If B=A∪C, then A=B-C.
f.) |A-B|=|A|-|B|.
g.) (A-B)∪B=A.
h.) (A∪B)-B=A.
Simply stating why each is true or false would be fine. Explanations always help, however.
This may become a periodical thread. Thanks for the help.