Math 61 Practice First Test

Math 61 Practice - Practice First Test Mathematics 61 Disclaimer Listed here is a selection of the many possible sorts of problems actual test is

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Practice First Test Mathematics 61 Disclaimer: Listed here is a selection of the many possible sorts of problems. The actual test is apt to make a different selection. 1. Let S5 be the set of all binary strings of length 5 (such as 11001). Let E be the equivalence relation on S5 for which sEt if and only if s and t have the same first three bits. (For example, 11011 E 11010.) (a) Find [10101], the equivalence class of the string 10101. (b) How many equivalence classes are there altogether? (Support your answer.) (c) Let A = {4, 5, 6, 7} and let P = {{5, 7}, {4, 6}}. Then P is a partition of A. Give the matrix (relative to numerical order on A) of the equivalence relation R on A for which A/R = P. 2. (a) Assume that R is a transitive relation. Show that whenever (x, y) is in R o R, then (x, y) is also in R. (b) Assume that Q is a relation and that Q o Q is a subset of Q. Prove that Q is transitive. 3.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/20/2008 for the course MATH 61 taught by Professor Enderson during the Fall '08 term at UCLA.

Page1 / 3

Math 61 Practice - Practice First Test Mathematics 61 Disclaimer Listed here is a selection of the many possible sorts of problems actual test is

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online