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###### Discrete Mathematics (pages 40, 41)

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"Sets" Review Assignment

*1.*What is a set?*2.*What does the following set mean: \(A = {1, 15, 35}\)*3.*Explain why the following notation doesn't make sense: \(d \in {a, b, c}\)*4.*Consider the sets \(A = {1, 15, 35}\) and \(B = {1, 15}\). Is it fair to say that \(B \in A\)? Why or why not?*5.*Describe the following set: \({x : x+ 3 \in \mathbb{N}}\)*6.*Define the following special sets:

- a. \(\emptyset\)

- b. \(\mathcal{U}\)

- c. \(\mathbb{N}\)

- d. \(\mathbb{Z}\)

- e. \(\mathbb{Q}\)

- f. \(\mathbb{R}\)

- g. \(\mathcal{P}(A)\)*7.*What's the cardinality of the following set: \(A={3,4,…,20}\)*8.*Consider the following sets: \(A = {1, 2, 3, 4, 5, 6}\) and \(B = {2, 3}\). Is \(A \subset B\) true or false?*9.*Consider the set \(A = {a, b, c}\). What's the power set of \(A\), \(\mathcal{P}(A)\)?*10.*What is the union of two sets?*11.*What is the intersection of two sets?*12.*Consider the sets \(A={1,2}\) and \(B={3,4,5}\). What is the Cartesian product, \(A \times B\)?

Levin, O. (2018-12-31). Discrete Mathematics: An Open Introduction. . (Sep 10, 2023)

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