This document provides the questions for Assignment 5 in the course WUCT121: Discrete Mathematics at Wollongong College Australia for Autumn 2011. It consists of 8 questions covering topics like sets, relations, modular arithmetic, probability, and pigeonhole principle. Students are instructed to show working for all answers and submit the assignment before the beginning of their tutorial in week 11.
This document provides the questions for Assignment 5 in the course WUCT121: Discrete Mathematics at Wollongong College Australia for Autumn 2011. It consists of 8 questions covering topics like sets, relations, modular arithmetic, probability, and pigeonhole principle. Students are instructed to show working for all answers and submit the assignment before the beginning of their tutorial in week 11.
This document provides the questions for Assignment 5 in the course WUCT121: Discrete Mathematics at Wollongong College Australia for Autumn 2011. It consists of 8 questions covering topics like sets, relations, modular arithmetic, probability, and pigeonhole principle. Students are instructed to show working for all answers and submit the assignment before the beginning of their tutorial in week 11.
This document provides the questions for Assignment 5 in the course WUCT121: Discrete Mathematics at Wollongong College Australia for Autumn 2011. It consists of 8 questions covering topics like sets, relations, modular arithmetic, probability, and pigeonhole principle. Students are instructed to show working for all answers and submit the assignment before the beginning of their tutorial in week 11.
Please staple your assignment together, with this cover sheet. Give full working for all answers, unless the question says otherwise. Untidy or badly set-out work will not be marked, and will be recorded as unsatisfactory. This assignment must be submitted before the beginning of your tutorial in week 11.
Question 1.
Let A = {a1, a2, a3} and B = {b1, b2}.
How many elements are there in A x B?
Question 2.
Let U be the universal set of all letters of the English alphabet. Let A = {r, t, x, y, z} and B = {u, v, w, x, y, z}. List all the elements of the following sets: (a) A B (b) A B (c) A B (d) B A (e) (f)
Question 3.
Let A = {1, 2}, B = {1, 3}, and C = {2, 3}.
(i) Write down the elements of (A B) x C and (A x C) (B x C). What do you notice? (ii) Write down the elements of (A B) x C and (A x C) (B x C). What do you notice?
Question 4.
Determine which of the following congruence relations are true and which are false: (i) 17 2 (mod 5) ; (ii) 4 5 (mod 7 ) ; (iii) 2 8 (mod 3) ; (iv) 6 22 (mod 2) .
Date submitted: ______________________________________ Tutor initials: ________________
Page 1 of 2 Question 5.
(a) Write out the addition and multiplication tables for Z5. (b) Use the tables in part (a) to solve the equations below for x in Z5: (i) x + [3] = [1] ; (ii) [2] x = [3] ; (iii) [3] x = [1] ; (iv) x + [4] = [0] . (c) For each element of Z5 find its additive inverse (if it exists). (d) For each non-zero element of Z5 find its multiplicative inverse (if it exists.)
Question 6.
Find 916 (mod 11).
Question 7. How many people must attend a college to ensure that at least 3 people have a surname that begins with the same two letters? Question 8. In a group of 30 people, must at least 4 have been born in the same month? Justify your answer.
