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1.)
a) Disprove by giving a counterexample that for any sets A,B,C, A∩(B∪C) = (A∩B)∪C.
b) Prove that (B -A)∪(C -A) = (B ∪C)-A. First show that every element on the left side belongs to the right side, then show that every element from the right side belongs to the left side, using de?nitions of union and difference.
c) Let g: A → B and f : B → C be one-to-one functions, where A, B, C are arbitrary sets. Prove that their composition f ?g: A → C is a one-to-one function.
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In each of represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b).
Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
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