2345_2019-Spring-HW3-Sets-Solutions.pdf - Math 2345 \u2013 Discrete Mathematics Homework 3 Introductory Set Theory Solutions Due Date Wednesday(beginning

# 2345_2019-Spring-HW3-Sets-Solutions.pdf - Math 2345 u2013...

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Homework 3: Introductory Set Theory Solutions Math 2345 – Discrete Mathematics Homework 3: Introductory Set Theory Solutions Due Date: Wednesday, February 20, 2019 (beginning of class) Complete the following problems. Show all work and explain your reasoning carefully where appropriate. Justify your arguments and supply evidence to back up your claims. I will not accept late homework without a valid reason. Throughout, Z (integers), N (natural numbers), Q (rationals), R (reals), P (primes), B n (bitstrings of length n ), and P ( A ) (power set of A ). Problem 3.1 (Elements of Sets).(a) Write each of the following sets by explicitly listing all of their elements.i.{nN: 1n20andn+ 1is prime}ii. The set of bitstrings of length four where no two ones are separated by any zeros.iii.C={yZ:y2= 2}iv.B={nZ:n3-n= 0}(b) Consider the setA={{1,2,},1,,{1},{1,2}}.i. How many elements doesAhave?ii. True or False:1∈ {1}and{1} ∈A.iii. True of False:Aand{} ∈ {1,2,}.iv. True or False:2∈ {1,2}and2A.Solution 3.1.(a)i.{1,2,4,6,10,12,16,18}ii.{1111,1110,0111,1100,0110,0011,1000,0100,0010,0001,0000}iii.iv.{0,-1,1}(b)i.5ii. Trueiii. Falseiv. FalseProblem 3.2 (Subsets).(a) List the subsets of{1,Z,{1}}.(b) LetA={{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}.i. Give an example of a subset ofAthat has one element.ii. Give an example of a subset ofAthat has three elements.(c) Give examples of three different nonempty finite sets,A,B, andCthat satisfy the following.i.AB,BC, andAC.ii.AB,AC, andB6⊂C. Solution 3.2.
Homework 3: Introductory Set Theory Solutions