2. MODULE 1: WHAT IS A
SET?
•A set is a well-defined
collection of objects.
3. Column A Column B
Collection of:
• positive integers
• math books in a
library
• names of students in
school
• provinces in the
Philippines
Collection of:
• rich people
• large animals
• nice objects
• bright students
4. •In column A, each
collection is well-defined
because one can identify
if an object belongs to the
collection or not.
5. •In column B, phrases like
“rich people”, “large
animals”, “nice objects” &
“bright students” are not
well-defined because
these are subjective
phrases.
6. Which of the following collections
are sets and which are not?
1. Collection of round objects
2. Collection of animals with
tails
3. Collection of small boxes
7. WHAT IS AN ELEMENT?
•An element is an
object or item that is
contained in the set.
Ex: A={s, t, u, d, y}
8. SYMBOLS
•Braces { } -are used to
enclose the elements
of a set.
Ex: A={s, t, u, d, y}
9. SYMBOLS
•∈ means “is an element
of”.
Ex:
s∈A
y∈A
“s is an element of A”
“y is an element of A”
10. SYMBOLS
•∉ means “is not an
element of”.
Ex:
b∉A
x∉A
“b is not an element of A”
“x is not an element of A”
11. SYMBOLS
•{ } – means empty set
• ∅ - means null set
Ex: Set Y is a set of blue mangoes.
Y= { } or Y=
∅
12. MODULE 2: WHAT ARE
THE TYPES OF SETS?
•Consider that sets 𝑈, 𝐴, and 𝐵:
𝑈 = {𝑥|𝑥 𝑖𝑠 𝑎𝑛 𝑎𝑛𝑖𝑚𝑎𝑙 𝑜𝑛 𝑙𝑎𝑛𝑑}
𝐴 = 𝑑𝑜𝑔, 𝑐𝑎𝑡, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒, 𝑚𝑜𝑛𝑘𝑒𝑦
𝐵 = 𝑑𝑜𝑔, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒
13. •Set 𝑈 is considered as
𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑎𝑙 𝑆𝑒𝑡.
•It is the set containing all the
elements of all other sets.
𝑈 = {𝑥|𝑥 𝑖𝑠 𝑎𝑛 𝑎𝑛𝑖𝑚𝑎𝑙 𝑜𝑛 𝑙𝑎𝑛𝑑}
𝐴 = 𝑑𝑜𝑔, 𝑐𝑎𝑡, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒, 𝑚𝑜𝑛𝑘𝑒𝑦
𝐵 = 𝑑𝑜𝑔, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒
14. •Set 𝐴 and Set 𝐵 are subsets
of Set 𝑈. Therefore,
and
𝑈 = {𝑥|𝑥 𝑖𝑠 𝑎𝑛 𝑎𝑛𝑖𝑚𝑎𝑙 𝑜𝑛 𝑙𝑎𝑛𝑑}
𝐴 = 𝑑𝑜𝑔, 𝑐𝑎𝑡, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒, 𝑚𝑜𝑛𝑘𝑒𝑦
𝐵 = 𝑑𝑜𝑔, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒
15. •Set 𝐵 is a proper subset of
Set 𝐴 because Set 𝐴 has
elements that are not in Set
𝐵. In symbol, .
𝑈 = {𝑥|𝑥 𝑖𝑠 𝑎𝑛 𝑎𝑛𝑖𝑚𝑎𝑙 𝑜𝑛 𝑙𝑎𝑛𝑑}
𝐴 = 𝑑𝑜𝑔, 𝑐𝑎𝑡, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒, 𝑚𝑜𝑛𝑘𝑒𝑦
𝐵 = 𝑑𝑜𝑔, 𝑐𝑎𝑟𝑎𝑏𝑎𝑜, 𝑒𝑎𝑔𝑙𝑒
16. 2 METHODS OF
WRITING SETS
1. ROSTER METHOD- listing
of elements.
2. SET-BUILDER METHOD-
describing the elements.
17. EXAMPLE
ROSTER METHOD SET-BUILDER METHOD
1. A = a, b, c, d, e 1. A={x | x is one of the
first 5 letters of the
English Alphabet}
2. B = 1, 3, 5, … , 19 2. B={x | x is an odd
number less than 20}
3. C = 2, 4, 6, 8 … 3. C={x | x is an even
number}
