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Question: if you could also explain the symbols for me too...

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If you could also explain the symbols for me too that would greatly be appreciated.

Homework Assignment # 1 (Chapter 1) Name: MHF 2191: Mathematical Foundations December 19, 2018 Question 1 (10 points) 1.2 Let S -2,-1,0,1,2,3). Describe each of the following sets as fESp()), where p(x) is some condition on x (a) A (1,2,3 (b) B= {0.1.2.3) (c) C= {-2,-1} (d) D -2,2,3) Proof. QED Question 2 (10 points) 1.8 (a) Describe the set A by listing its elements (b) Give an example of three elements that belong to B but do not belong to A (c) Describe the set C by listing its elements. (d) Descibe the set D in another manner (e) Determine the cardinality of each of the sets A, C, and L Proof. QED Question 3 (10 points) 1.28 Let A, B, and C be nonempty subsets of a universal set U. Draw a Venn diagram for each of the following set operations (a) (C- B)U A (b) Cn(A- B)Here is an example of a Venn diagram in ETEX. Proof. QED Question 1 (10 points) 1.40 For i C Z, let A-i 1,). Determine the following (b) U1 (A, n A) Proof. 2i+1 QED Question 5 (10 points) 1.42 For cach of the following collections of sets, define a set An for each nEN such that the indexed collection (An} EN ls precisely the given collection of sets. Then find both the union and the intersection of the indexed collection of sets Proof. Question 6 (10 points) QED 1.52 Give an example of a partition of N nto three subsets. Proof QED Page 2

Question 7 (10 points) 1.66 For A-(1.2) and B = {1}, determine P (A × B) Proof QED Question 8 (10 points) 1.78 Let l_ {1, 2, 3} be the universal set and let A-{1.2], B-(23), and C-{13) Determine the following: (a) (AUB) (BnC) (b) A (c) BUC (d) Ax B Proof. QED Question 9 (10 points) 1.88 Give an example of a set A -{1,2,... ,k) for a smallest k E N containing subsets Ai . A2, Аз such that Ai-Al-A,-AJ-li-j for every two integers i and j with Proof. QED Question 10 (10 points) 1.93 (a) Us, (b) ns. Proof. QED Page 3

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