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Discrete Math : Counting and Relations

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Basics of Counting
32. How many functions are there from the set {1, 2, ... , n}, where n is a positive integer, to the set {0, 1}?

Relations & Relation Properties
24. Let R be the relation R = {(a, b) | a < b} on the set of integers. Find
a) R -1
b) bar-R

Application of Relations
8. Suppose that R is a symmetric relation on a set A. Is bar-R also symmetric?

Please see the attached file for the fully formatted problems.

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For each topic, demonstrate a knowledge and capability by giving the following information:

1) Problem Solution: (solution for an even number problem) see below...

2) Personal Observation: (personal comment on the topic including advice to others on how to study and understand it).

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Counting and relations are investigated. The solution is detailed and well presented.

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