Study Guides (247,962)
Canada (121,191)
CPSC 233 (11)
Tony Tang (9)
Quiz

MATH271Quiz3Solutions.pdf

1 Page
106 Views
Unlock Document

Department
Computer Science
Course
CPSC 233
Professor
Tony Tang
Semester
Winter

Description
1 MATHEMATICS 271 L01 WINTER 2014 Quiz 3 Solutions [7] 1. Prove statement (a) by contradiction, and disprove the statement (b) by writing out its negation and prove that. (a) For all sets A;B and C, if C ▯ B ▯ A then A \ C = ;. Solution: Let A;B and C so that C ▯ B ▯ A. We prove A \ C = ; by contradiction. Suppose that A \ C 6= ;; that is, there exists an element x 2 A \ C. Since x 2 A \ C, we know x 2 A and x 2 C. Since x 2 C and C ▯ B ▯ A, we get x 2 B ▯ A, and so we have x = A. Thus, we have the contradiction x 2 A and x 2 = A. Therefore, A \ C = ;. (b) For all sets A;B and C, if A ▯ B ▯ C and B ▯ C ▯ A then C ▯ A ▯ B. Solution: The negation of this statement is: \There are sets A;B and C so that A▯B ▯ C and B ▯ C ▯ A, but C ▯ A * B." For example, consider the sets A = B = ; and C = f1g. In this case we have A▯B = ;▯B = ; ▯ C and B▯C = ;▯C = ; ▯ A but C▯A = C▯; = C = f1g * ; = B. [8] 2. For each of the following questions, give a brief explanation on how you get the answers. (a) How many positive four-digit integers can be formed using only the digits 1,2,3,4,5,6,7,8,9? 4 Solution: There are 9 such numbers since we have 9 choices for each of the four digits of the numbers. (b) How many integers in part (a) have the property that the digit 1 appears at least once? Solution: The answer to this question is 9 ▯ 8 , that is the total number of the integers in (a) minus the number of integers without 1. The number of integer
More Less

Related notes for CPSC 233

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit