3. MELC
• Illustrates the union and intersection of sets and the
difference of two sets.
•Illustrates and describes the union of two sets.
•Illustrates the difference of two sets •Illustrate the
complement of a set.
WEEK 1- MELC 1
4. Describe well-defined sets, null set, cardinality
of sets, union and intersection of sets, and
difference of two sets
Find the union, intersection and
complement of sets
Appreciate the importance of sets
5. What is a set?
1. Set is a well-defined collection of distinct objects or ideas,
called elements, that are defined by common characteristics or
attributes.
2.Set is a well-defined list, collection or class of objects.
3. Sets may be named by using capital letters and small letters
for the elements.
6. What is a set?
4. Elements of the set can be listed within the braces.
5. Elements should be distinct, there must be no repetition of
elements in a set.
7. What is a SUBset?
The set F is a subset of set A if all elements of F are also
elements of A. For example, the even numbers 2, 4 and 12 all
belong to the set of whole numbers. Therefore, the even
numbers 2, 4, and 12 form a subset of the set of whole
numbers. F is a proper subset of A if F does not contain all
elements of A.
8. What is a universal set?
. The universal set U is the set that contains all
objects under consideration. The set of all letters
in the alphabet could be a universal set from
which the set {a,b,c,d,…..z} could be taken.
9. Task 1: where do I belong?
Given a set of pictures of some objects. Group them as many as you can and label
each group.
10. 6 Basic Animal Groups (thoughtco.com)
Invertebrates are characterized by
their lack of backbones and
internal skeletons as well as their
relatively simple anatomy and
behavior, at least compared with
those of most vertebrates.
The first true vertebrates on Earth, fish
evolved from invertebrate ancestors about
500 million years ago and have dominated
the world's oceans, lakes, and rivers ever
since.
Amphibians are
characterized by their semi-
aquatic lifestyles (they must
stay near bodies of water to
maintain the moisture of
their skin and to lay eggs),
and today they are among
the most endangered
animals in the world.
Birds are characterized by
their coats of feathers, their
warm-blooded
metabolisms, their
memorable songs (at least
in certain species), and
their ability to adapt to a
wide range of habitats
Reptiles are characterized
by their cold-blooded
metabolisms—they fuel
themselves by exposure
to the sun—their scaly
skin, and their leathery
eggs, which they, unlike
amphibians, can lay some
distance from bodies of
water.
Mammals are characterized by their hair or fur, which all species possess during some
stage of their life cycles; the milk with which they suckle their young, and their warm-
blooded metabolisms, which, as with birds, allows them to inhabit a wide range of
habitats, ranging from deserts to oceans to arctic tundra.
11. Task 2: all are possible
Identify all the possible answers for the statements below
1. All the provinces in Region IV-A
2. Numbers greater than 8.
3. All subjects in Grade 7.
4. Vowels in the English alphabet.
5. Five animals with four legs.
12. QUESTIONS
1. How many groups are there?
2. Does each object belong to a group?
3. Is there an object that belongs to more than
one group? Which one?
13. Different ways of describing sets
1. By definition such as the set of counting the members of a set.
2. By listing each member of a set like 1, 2, 3, 4, 5, …
3. By set notation such as Primary color = { red, yellow, blue}.
14. Example 1
Describe the elements of each set
4 6 8 10
12
SET A
The set of even numbers from 4 to
12.
1 2 3 4 5
6
SET B
The set of counting numbers from
1 to 6.
15. Example 1
Describe the elements of each set
SET C
The null set/ empty set.
1 2 3 6 9
18
SET D
The set of factors of 18.
17. Set operations
*In set theory, the union
(denoted by ∪) of a
collection of sets is the set of
all distinct elements in the
collection.
Union of sets
*Given two sets A and B, the union is the set that
contains elements or objects that belong to either
A or to B or to both
We write A U B
20. Set operations
The intersection of two sets A
and B is the set of elements
common to both A and B
Intersection of sets
The symbol is an upside down "U" like this: ∩
We write A ∩ B
21. Set operations
the set of all elements common to both sets A and B.
Intersection of sets
23. ACTIVITY 1 Using the figure, find the elements found in the
indicated sets.
24. Set operations
The number of elements in a set
Cardinality of sets
1. Let A be a set. If A = (the empty set), then the cardinality of A is
0. b.
2. If A has exactly n elements, n a natural number, then the
cardinality of A is n. The set A is a finite set.
3. Otherwise, A is an infinite set.
25. Set operations
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.
Complement of a set
The complement of any set is represented as A', B', C'
etc. In other words, we can say, if the universal set is
(U) and the subset of the universal set (A) is given then
the difference of universal set (U) and the subset of the
universal set (A) is the complement of the subset, that is
A' = U - A.
26. Set operations
Difference of a set
The difference of two sets, written as A – B, is the set of all
elements of A that are not elements of B.
