Question 1 (10 marks)
(i) Write the statement Each MATH121 student will pass at least one MATH121 assignment
using quantiers. Do you think that this statement is true?
(ii) Write the statement x R, y
Lecture 11
Relations and Functions 3
This material is covered in Section 5.5 of the course notes.
Recap (Lecture 10)
Suppose A is a set and R is an equivalence relation on A. For
each a A, the equival
Lecture 8
Set Theory 2
This material is covered in Sections 4.4.14.6 of the course notes.
Recap (Lecture 7)
A set is just a collection of objects. The objects are called
elements.
The empty set is the
Lecture 9
Relations and Functions 1
This material is covered in Sections 5.15.3 of the course notes.
The Cartesian Product
Denition. Let A and B be sets, and let a A and b B . An
ordered pair (a, b )
Lecture 10
Relations and Functions 2
This material is covered in Section 5.4 of the course notes.
Recap (Lecture 9)
If A and B are sets, then the Cartesian product of A and B ,
denoted A B , is A B =
Lecture 4
Predicate Logic
This material is covered in Section 2 of the course notes.
Introduction to Predicate Logic
In the last three lectures we discussed the logical analysis of
compound statements
Question 1 (12 marks)
(i) Prove that if a, b Z and a | b or a | c, then a | bc.
(ii) Prove that the product of an odd integer and an even integer is even.
(iii) Write down all the positive divisors of
Question 1 (10 marks)
(i) Write the statement Each MATH121 student will pass at least one MATH121 assignment
using quantiers. Do you think that this statement is true?
(ii) Write the statement x R, y
Lecture 5
Methods of Proof 1
This material is covered in Sections 3.13.2.2 of the course notes.
Logic Recap
Let P and Q be statement variables. Then
P
means
P Q
means
P Q
means
P = Q
means
P Q
means
L
Lecture 1
Logic 1
This material is covered in Sections 1.11.2.3 of the course notes.
Introduction to logic
Arithmetic is the study of numbers and the operations addition,
subtraction, multiplication a
Lecture 6
Methods of Proof 2
This material is covered in Sections 3.2.33.5 of the course notes.
Recap (Lecture 5)
An argument is a sequence of statements. All the statements
in an argument apart from
Lecture 2
Logic 2
This material is covered in Sections 1.2.41.3.2 of the course notes.
Recap (Lecture 1)
A statement is a sentence that is true or false but not both.
New statements are formed from ol
Lecture 3
Logic 3
This material is covered in Sections 1.3.31.4.2 of the course notes.
Recap (Lecture 2)
The conditional of Q by P is If P , then Q or P implies Q
and is denoted P = Q .
The biconditi
Lecture 7
Set Theory 1
This material is covered in Sections 4.14.4 of the course notes.
Introduction to sets
The words set and element are undened terms of set theory
just like the terms sentence, tru