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Understanding Complements as a Set

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. 



 The diagram above shows a Venn Diagram and what information you are suppose to look out for or input when constructing a two (2) set diagram.

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

Unknown said…
1. (Monday, Tuesday, Wednesday, Saturday, Sunday)
2. A’( 1,6,7,8,11,12,15,16)
3. B’( 2,4,6,7,8,9,10,16)
October 30, 2022 at 3:43 PM
Unknown said…
Q'= {Monday, Tuesday, Wednesday, Saturday, Sunday}

A'={1, 6, 7, 8, 11, 12, 15, 16}
B'={2, 4, 6, 7, 8, 9, 10, 16}
October 31, 2022 at 12:13 PM
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