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MBA IT, Mater in Science and Technology
Devry
Jul-1996 - Jul-2000
Professor
Devry University
Mar-2010 - Oct-2016
Here are my advanced math homework. Please help me with my homework. Thank you very much.
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1. (4 pts) Prove the following identity for sets:A × (BC) = (A × B)(A × C).(You may either use logical equivalences or show that each side is a subset of the other).
2. (4 pts) Prove that for any sets A and B, P(A) ∪ P(B) ⊆ P(A ∪ B). Is it always true thatP(A ∪ B) ⊆ P(A) ∪ P(B)?
3. (4 pts) Prove parts c and d of Theorem 2.2 in the notes on sets.
4. Let f : Z → Z be defined by f(n) = 3n + 2.a. (1 pt) Is the range of f equal to Z? Justify your answer.b. (1 pt) Find the image of E = {−2, −1, 0, 1, 2}.c. (1 pt) Find the pre-image of H = {2n : −4 ≤ n ≤ 4}.
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Math 3000 - Assignment 2 : Due Friday Sept 9, in class (15 pts)
1. (4 pts) Prove the following identity for sets:
A × (B\C) = (A × B)\(A × C).
(You may either use logical equivalences or show that each side is a subset of the other).
2. (4 pts) Prove that for any sets A and B, P(A) ∪ P(B) ⊆ P(A ∪ B). Is it always true that
P(A ∪ B) ⊆ P(A) ∪ P(B)?
3. (4 pts) Prove parts c and d of Theorem 2.2 in the notes on sets.
4. Let f : Z → Z be defined by f (n) = 3n + 2.
a. (1 pt) Is the range of f equal to Z? Justify your answer.
b. (1 pt) Find the image of E = {−2, −1, 0, 1, 2}.
c. (1 pt) Find the pre-image of H = {2n : −4 ≤ n ≤ 4}.
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