WELCOME Grade 9-11 Students
In today's blog we will learn about the complements as a set.
Objective:
·
At
the end of this reading, students will be able to use the notation A and A' to
represent the complement of sets.
·
Use
Venn diagrams to identify the complements of sets
Venn Diagrams
A Venn diagram is drawn by using
a rectangle to represent the universal set and circles inside the rectangle to
represent its subsets.
Below is a video showing how to construct a Venn diagram with 2 sets.
The Complement
The complement of a set is the
set that includes all the elements of the universal set that are not present in
the given set. The symbol used to identify a complement could be Ac or A'.
Example,
If U= {pupils in my school} and X=
{pupils who represent the school at games} then the complement of X is the set
of all the members of U that are not members of X. In this case, the complement of X is {pupils
in my school who do not represent the school at games}.
Another example,
If U= {the whole numbers from 1
to 10 inclusive} and A= {odd numbers between 1 and 10} then the complement of A or A' is {2, 4, 6, 8, 10} which you know that these are even numbers.
The diagram below shows that the shaded region represent the complement of the given set.
Practice Questions
1. Given the complements of Q where Q=
{Thursday, Friday} if U= {days of the week} then what is Q'.
2. From the diagram below, find
a. A'
b. B'
Comments
2. A’( 1,6,7,8,11,12,15,16)
3. B’( 2,4,6,7,8,9,10,16)
A'={1, 6, 7, 8, 11, 12, 15, 16}
B'={2, 4, 6, 7, 8, 9, 10, 16}