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Set Theory Problems Solutions - MIT

JHU-CTY Theory of Computation (TCOM) Lancaster 2007 ~ Instructors Kayla Jacobs & Adam GroceSET Theory PROBLEMSSOLUTIONS * (1) Formal as a Tux and Informal as JeansDescribe the following sets in both formal and informal Set Notation DescriptionInformal English Descriptiona){2, 4, 6, 8, 10, ..}The set of all positive even integersb){.., -3, -1, 1, 3,..}The set of all odd integersc){n | n = 2m for some y }The set of all positive even integers(using the convention that 0 is not a natural number)d){x | x=2n and x=2k for some n, k }The set of all positive multiples of 6e){b | b and b=b+1} f){2, 20, 200} The set containing the numbers 2, 20, and 200g){n | n and n > 42}The set containing all integers greater than 42h){n | n and n < 42 and n > 0} = {n | n and n < 42}The set containing all positive integers less than 42i){ hello } The set containing the string helloj){ bba , bab } The set containing the strings bba and babk) = {} The set containing nothing at alll){ } The set containing the empty string1 JHU-CTY Theory of Computation (TCOM) Lancaster 2007 ~ Instructors Kayla Jacobs & Adam Groce* (2) You Want Me to Write What?

SOLUTIONS * (1) Formal as a Tux and Informal as Jeans Describe the following sets in both formal and informal ways. Formal Set Notation Description Informal English Description a) {2, 4, 6, 8, 10, …} The set of all positive even integers b) {…, -3, -1, 1, 3,…} The set of all odd integers

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