Sets

SETS

​By : kasskassmaths

​General Mathematics Syllabus

​Section 3, Objectives 1 - 8

TABLE OF CONTENTS

​

​​Representation of a set - Slide 3

Concepts / Definitions - Slide 6

​Venn Diagrams - Slide 8

​Relationship among sets :

Intersection - Slide 9

​Subset - Slide 11

​Disjoint - Slide 13

Worked Past Paper Questions (P2's) - Slide 15

Past Paper Questions to Practice (P1's) - Slide ​19

Representation of a set

CONCEPTS / DEFINTIONS

6)Universal set ​: this is the set from which all elements are taken. It is denoted by the symbol U.

​7)Empty / null set : this is a set that contains no elements and is denoted by the symbol ∅ or {}.

​8)Complement : the complement of a set is the set of all elements in the universal set that is NOT contained in a specific set. The symbol ' is placed after the set name to represent the complement.

E.g. Given U = {2,4,6,8} and K = {2,4}. The complement of K, represented as K' is {6,8}.

​

Venn Diagrams

Venn diagram - a diagram that represents sets and set problems using circles and a rectangle.

In drawing venn diagrams, the rectangle represent the universal set (U) and the circle(s) represent(s) a subset(s). ​Hence the circle(s) are drawn inside of the rectangle.​ Any members or elements outside of the circle(s) but within the rectangle, represents the complement.

​

​

​

​

​The yellow represents the complement of set T.

​U

​T

Relationship among sets (Venn diagrams)

​

​2

​

​

​1

3​

​9 12

​2 4

5

​B

​A

​13

​U

​E.g. Represent the following on a venn diagram.

​U = {1,2,3,4,5,6,7,8,9,10}

A = {1,2,3,4,5}

B = {3,4}​

​E.g. Represent the following on a venn diagram.

​U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {​0, 1, 2, 3}

Q = {8, 9, 10}​

​

​

​

​4 5 6 7​

​8 9

​10

​0 1

​2 3

​Q

​P

​U

June 2017 P2 # 3(a)

​The universal set U is defined as follows :

​U = {x : x ∈ N, 2 < x < 12}.

The sets M and R are subsets of U ​such that :

​M ={odd numbers}

R = {square numbers}​

(i) List the elements in the subset M.

(ii) List the elements in the subset R.​

(iii) Draw a venn diagram ​that represents the relationship among the defined subsets of U.

​(i) M = {3,5,7,9,11}

​(ii) R = {4,9}

​(iii)

June 2016 P2 #3(a)

​The venn diagram below shows the number of students who study History and French in a class of 30 students.

U = {students in class} H = {students who study History}

F = ​{students who study French}

​Total number of student in class is 30, therefore 37 - x = 30.

solving for x :

37 - x = 30

37 - 30 = x

7 = x​

x = 7

​

Past Paper Questions to Practice

Jan 2024 P1 Nos. 7 - 12
June 2023 ​P1 Nos. 7 - 12
Jan 2023 P1 Nos. 7 - 12
Jan 2022 P1 - Nos 7 - 12

​Jan 2020 P1 - Nos 7 - 12

​May 2021 P1 - Nos 7 - 12

​May 2019 P1 - Nos 7 - 12