Brock University

• MATH 1P66

• BROCK UNIVERSITY Final Examination: June 2013 Course: Math 1P66 Date of Examination: Friday. ,June 7, 2013 Time of Examination: 1200-1500 Page 1 of 10 Number of pages: 10 Number of students: 88 Number of hours: 3 Instructor: Basil Nanayakkara 1 Answer each question in the space provided. Use the reverse side for rough work. The marks for each question are shown in the left margin. Calculators and other electronic devices are prohibited. A minimum of ,10% must be obtained on this final examination in order to achieve a passing grade in the course. Total ~Iarks: 100 NAME: _________________ ,Student Number: ___________ _ Course: MATH 1P66 Exam date: June 7, 2013 page 2 (1 point) 1. (a) Find the truth value of the statement 3x(x = 1), where the domain for x is all real numbers. (1 point) (b) Find a counterexample to Vx(x2 > x) where the domain for x is all integers. (4 points) (c) Determine the truth value of the following, where the domain for x and for y is all real numbers. (2 points) (2 pints) (2 points) (2 points) (2 points) (1 point) (2 points) (2 points) i. V£jy(x2 = y) ii. 3yV:r(x2 = y) iv. :JxVy(x2 = y) (d) Let A and B be sets such that IAI = 10, IBI = 19 and IA n BI = 5. What is the cardinality of AuB? (e) Find the power set of {a.b}. (f) Find the symmetric difference of A and B where A = {D, 3,1. 2} and B = {l, 7l"}. (g) Finel the truth value of ¢