Download INEQUALITIES

A set is a well-defined collection of any kind of
objects: people, ideas, plants, numbers, responses,
etc.
e.g.
1. M is a set of Math teachers at SMP Madania.
2. P is a set of prime numbers less than 10.
3. _______________________________________________
4. _______________________________________________
5. _______________________________________________
A. LISTING THE ELEMENTS
1. M is the set Math teachers at the Lower Secondary Madania.
M = {Icha, Tiyan, Wati}
2. P is the set of whole numbers less than 4.
P = {0, 1, 2, 3}
3. ________________________________________________
__ = {________________________}
4. ________________________________________________
__ = {________________________}
5. ________________________________________________
__ = {________________________}
NOTATION FOR SETS
B. WRITING THE PROPERTY CHARACTERIZING THE ELEMENTS
1. M is the set Math teachers at SMP Madania.
M = {x|x is a Math teacher at SMP Madania}
2. P is the set of whole numbers less than 4.
P = {x|x < 4, x  whole numbers}
3. _________________________________________________
__ = {x|x ___________________________}
4. _________________________________________________
__ = {x|x ___________________________}
5. _________________________________________________
__ = {x|x ___________________________}
1. M is the set of Math teachers at SMP Madania.
M = {Icha, Tiyan, Wati}
M = {x|x is a Math teacher at SMP Madania}
→”M is the set of all people x such that x is a Math
teacher at SMP Madania.”
2. P is the set of whole numbers less than 5.
P = {0, 1, 2, 3, 4}
P = {x|x < 5, x  whole numbers}
→” P is the set of all numbers x such that x is less
than 5, x is element of whole numbers.”
3. ______________________________________________.
__ = {________________________________}
__ = {x|x ___________________________________}
→”__ is the set of all
x such that x is
.”
4. ______________________________________________.
__ = {________________________________}
__ = {x|x ___________________________________}
→”__ is the set of all
x such that x is
.”
A Venn diagram is a diagram where sets are represented
as simple geometric figures, with overlapping and
similarity of sets represented by intersections and
unions of the figures.

9
●1
●5
●7
●3
●9
●2
●6
●4
●8
What does this Venn diagram represent?

9
A
●1
●5
●7
●3
●9
A = The set of multiples of 3
between 0 and 10.
→ A = {3, 6, 9}
B
●2
●6
●4
●8
B = The set of even numbers
between 0 and 10.
→ B = {2, 4, 6, 8}
What do the symbols mean?
The set of all individuals in which you are
interested is called the universe .
UNIVERSE

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

9
A
●1
●5
●7
●3
●9
A = The set of multiples of 3
between 0 and 10.
→ A = {3, 6, 9}
B
●2
●6
●4
●8
B = The set of even numbers
between 0 and 10.
→ B = {2, 4, 6, 8}
What do the symbols mean?
ELEMENT
The objects belonging to a set are
called its members or elements.
&
NOT ELEMENT
3  A
9  B
 9
A
●1
●5
●7
●3
●9
B
4
●2
●6
●4
●8

B
2

A
What do the symbols mean?
COMPLEMENT
~A = {1,2, 4, 5, 7, 8}

A
●1
●7
~B = {1, 3, 5, 7, 9}

9
●5
The complement of a set A is the set of
all those elements of the universal set
which are not in A.
●3
●9
B
●2
●6
●4
●8
9
●1
●5
●7
B
●2
A
●3
●9
●6
●4
●8
What do the symbols mean?
DIFFERENCE
The difference of A and B means the
elements which belong to A but not to B.
A - B = {3, 9}
B - A = {2, 4, 8}


9
A
●1
●5
●7
●3
●9
B
9
●2
●6
●4
●8
A
●1
●5
●7
●3
●9
B
●2
●6
●4
●8
What do the symbols mean?
The intersection of two sets A and B is
the set whose elements are common to
both A and B.
INTERSECTION
= {6}
AB

9
●1
●5
●7
A
●3
●9
B
●2
●6
●4
●8
What do the symbols mean?
The union of two sets A and B is the set
which contains all the elements of A and
all the elements of B (and hence all the
elements which are in both A and B).
UNION
= {2, 3, 4, 6, 8, 9}
AB

9
●1
●5
●7
A
●3
●9
B
●2
●6
●4
●8
What do the symbols mean?
Set A is called a subset of set B if all
the elements of A are inside set B.
SUBSET
AB

9
●1
B
●4
●7
●9
●2
A
●5
●3
A = The set of multiples of 4
between 0 and 10.
→ A = {4, 8}
●8
●6
B = The set of even numbers
between 0 and 10.
→ B = {2, 4, 6, 8}
What do the symbols mean?
DISJOINT SETS
&
NULL/EMPTY SET
Ø
C // D

●4
●2 ●6
●8
D
●9
●7
●5
C = The set of even natural numbers
less than 10.
→ C = {2, 4, 6, 8}
D = The set of odd natural numbers
less than 10.
→ D = {1, 3, 5, 7, 9}
9
C
If C and D have no common elements, that is,
their intersection is the null set/empty set:
C  D = Ø,
then they are said to be disjoint sets.
●1
●3
What do the symbols mean?
EQUAL SET
S
Two sets A and B are said to be equal if
they contain exactly the same members.
E=F

E = The set of even numbers
between 0 and 10.
→ E = {2, 4, 6, 8}
9
E
F
●4
●2 ●6
●8
F = The set of multiples of 2
between 0 and 10.
→ F = {2, 4, 6, 8}
What do the symbols mean?
EQUIVALENT SET
S
E is equivalent
with G if the number of
elements in set E is the same as the
number of elements in G.
E~G

13
E
G
●4
●A
●2 ●6
●8
●B
●C
●D
E = The set of even numbers
between 0 and 10.
→ E = {2, 4, 6, 8}
G = The set of four first alphabets.
→ G = {A, B, C, D}
EQUIVALENT SETS
vs
EQUAL SETS
If A = B, then for sure A ~ B.
If A ~ B, then it is possible that A = B
PRESENTING
THE NUMBER OF ELEMENTS
IN A SET
e.g. A = {1, 2, 3, 4}
There are 4 elements in set A,
then it written as:
n(A) = 4