Sets and Subsets

1. (Sets and Subsets)

2. A different look at circles
 Set A Set B

Set C

3. In an excursion at Pagsanjan Falls, 80 students brought
sandwiches, drinks and canned goods as follows:
•50 students brought sandwiches
•30 students brought drinks
•30 students brought canned goods
•18 students brought canned goods and drinks
•15 students brought sandwiches and canned goods
•8 students brought sandwiches and drinks
•5 students brought sandwiches, canned goods and
drinks
Question:
How many students did NOT bring any of the 3 kinds?

4. SET
- a well
defined collection
of distinct objects
- CAPITAL
LETTERS are used
to represents set
Example:
A = {1, 2, 3, 4, 5}
B = { M, A, T, H}
C = { all even numbers}

5. ELEMENT
- pertains to
each object in a set
- denoted by the
symbol ______
which is read as
"element of set ____”
while the
symbol____means
“NOT an element of
set _____”
Example:
A ={ 1, 2, 3, 4, 5}
3 ____ of set A
7 _____ of set A

6. BRACES { }
- are used to
enclose the
elements of a
given set
Example:
A = { x | x is an even
integer}
Set is read as “the set of all
elements x, such that x is
an even integer”
B = { x | x is a letter in the

word Math}
“the set of all elements of
x, such that x is a letter
in the word Math”

7. A = {x | x is a multiple of 3
between 3 and 18 }
B = { x | x is a letter in the
word Algebra}
C ={ x | x is a positive odd
number }
A = { 3, 6, 9, 12, 15 }
B = {A, L, G, E, B, R }
C = {1,3, 5, 7, 9, 11, 13, ….}
ROSTER/LISTING
METHOD

8. Kinds of Sets:
FINITE SET
- a set whose
number of
elements can
be counted
Example:
A = { -1, -2, -3, -4, -5 }
B = { x | x is a multiple of
5 between 10 and 50}
C = { x | x is a letter in the
Philippine alphabet }

9. Kinds of Sets:
INFINITE SET
- a set whose
number of
elements
CAN NOT be
counted
Example:
A = { -1, -2, -3, -4, -5, . . . }
B = { x | x is a

multiple of 5 }
C = { x | x is a name
of a person}

10. Kinds of Sets:
NULL / EMPTY
SET
- a set that
has NO
element
- denoted by

{ } or O
Example:
A = { }
B = O

11. EQUIVALENT
SETS
- two or more
sets that have
the same
number of
elements
Example:
A = {2, 4, 6, 8, 10 }
B = { a, b, c, d, e}
Sets A and B are
equivalent sets.

12. EQUAL SETS
- two or more
sets that have the
same elements
Example:
A = {2, 4, 6, 8, 10 }
B = { 2, 4, 6, 8, 10 }
Sets A and B are
equal sets.

13. UNIVERSAL
SET
- the TOTALITY
of ALL the
elements in two
or more given
sets
- denoted by “U”
Example:
A = { 2, 4, 6, 8 }
B = { 1, 2, 3, 4 }
U = { 1, 2, 3, 4, 6, 8}
A = { a, b, c, d, e }
B = { a, e, i, o, u }
U = { a, b, c, d, e, i, o, u}

14. SUBSET
- Set B is a subset
of Set A if and
only if ALL the
elements in set B
is in Set A
Example:
A = { 2, 4, 6, 8 }
B = { 2, 4, 8 }
Set B is a subset of
Set A
A = { a, b, c, d, e }
B = { a, e, i, o, u }
Set B is NOT a subset
of Set A