MATH502程序写作、Mathematics程序

” MATH502程序写作、Mathematics程序Paper Code: MATH502Algebra and Discrete MathematicsAssignment 2Due 9:00am, Thursday, 14 May 2020Name …………………………………. Student Number ……………………..Stream Number …….Question Marks Possible Marks GivenInstructions:Please include this sheet as the first scanned page of your assignment. Submit completedsolutions via Blackboard, Under the Assessment link.Answer all questions and show your working. No working = no marks.This is an individual assignment. The point of the assignment is for you to go through the process ofdiscovery for yourself. Copying someone elses work will not achieve this. Plagiarism has occurredwhere a person effectively and without acknowledgement presents as their own work the work ofothers. That may include published material, such as books, newspapers, lecture notes or handouts,material from the internet Or other students written work.The School of Computer and Mathematical Sciences regards any act of cheating including plagiarism,unauthorised collaboration and theft of another students work most seriously. Any such actwill result in a mark of zero being given for this part of the assessment and may lead to disciplinaryaction.I understand the definition of plagiarism and I assert that this submission is my own work.Signature: ………………………………….Question 1 (12 marks). Let the Universal set, U = {x N | x 10}, A = {x | 2 x 8}, andB = {x | x 4}. (Note that 0 N.) Show the following sets by enumeration:a) A Bb) P(A B)c) {X | X (A B), 6 X}d) {X | X (A B) = }Question 2 (16 marks). Let U, A, B, C be as indicated in the diagram below:MATH502作业写作、Mathematics课程作业写作、Java，Python，C/C++程序语言作业辅导CDraw a Venn diagram and shade the area corresponding to each of the following. Show all workincluding any intermediate Venn diagrams as required.a) A (B C)b) (A B) Cc) A (B C)d) A (B C)Question 3 (6 marks). Use the set identities on the last page to prove any results indicated bythe Venn Diagrams in Question 2.Question 4 (12 marks). Let the universal set U = N P(N) and consider A = {0, 1, {2, 3, 4}},B = , and C = {1, 2}. What are the cardinalities of the following sets? Show all work.a) A Cb) C Bc) A Cd) C Be) P(A B)f) P(P(A))2Question 5 (16 marks). Consider the family of sets, Ak = {a N | a = kr, r N} where theindexing set S = {k N | k 0}. Prove the following:a) If m = ns, where s N, then Am An.b) The function fm,n : Am An Amn defined by fm,n(a, b) = ab is surjective.Question 6 (20 marks). For each of the following relations, determine if f is reflexive, symmetric, antisymmetric, or transitive.Conclude by stating if the relation is an equivalence, a partial order, or neither.For each point, state your reasoning in proper sentences.a) f = {(a, b) Z2| a b mod n, n Z}b) f = {(X, Y ) P(A)2| X Y }, where A is a non-empty setQuestion 7 (18 marks). For each of the following relations, determine if f is a function, surjective, or injective.Conclude By stating if the relation represents a bijective function.For each point, state your reasoning in proper sentences.a) f = {(a, b) N N2| a N, b N2, b = (a, 2a)}b) f = {(x, y) R2| y =x}Set IdentitiesA A = A Idempotent A A = AA B = B A Commutative A B = B A(A B) C = A (B C) Associative (A B) C = A (B C)A (A B) = A Absorption A (A B) = AA (B C) = (A B) (A C) Distributive A (B C) = (A B) (A C)A = A InvolutionA B = A B De Morgans A B = A BA B = A B DifferenceA = A Identity A U = AA U = U Domination A = A A = U Complement A A = 3如有需要，请加QQ：99515681 或邮箱：99515681@qq.com

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