VENN DIAGRAMS AND SET OPERATIONS p. 60-65

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					       VENN DIAGRAMS AND SET
         OPERATIONS p. 60-65

OBJECTIVES:

• Use Venn diagrams to visualize set relationships

• Perform operations with sets

• Apply set operations to the Real number system
Algebraic Expressions and Formulas, p. 270-276

OBJECTIVES:
•Evaluate algebraic expressions and formulas
•Understand the vocabulary of algebraic
expressions
•Simplify algebraic expressions
         Venn Diagrams p. 61

“Disjoint” sets have no   U
                              A       B
elements in common.

                          U       A
The set B is a “proper”
subset of A.                      B

                          U
The sets A and B have         A       B
some common elements.
Definition of Intersection of Sets p. 62


 The intersection of sets A and B, written
 AB, is the set of elements common to both
 set A and set B. This definition can be
 expressed in set builder notation as follows:
     A  B = { x | x  A AND x  B}
  Definition of the Union of Sets p. 63

The union of sets A and B, written A  B, is
the set of elements that are members of set A
or of set B or of both sets. This definition can
be expressed in set-builder notation as follows:
    A  B = {x | x  A OR x  B}
The empty set in intersection and union, p.64
For any set A,

 1. A    
  2. A    A

DeMorgan’s Laws, p.65
         
 A  B   A  B
         
 A  B   A  B
REAL NUMBERS – the set of numbers used to
measure or count things in everyday life.

Examples:
Natural numbers: {1, 2, 3, 4, …}
Whole numbers: {0, 1, 2, 3, 4, …}
Integers:          {…-3, -2, -1, 0, 1, 2, 3, …}
Rational numbers: {p/q | p and q are integers, q  0}
Irrational numbers: nonrepeating or nonterminating
                      decimals
Algebraic Expressions, p. 270

Variables- letters used to represent numbers.

Algebraic expression- a combination of
variables and numbers using the operations of
addition, subtraction, multiplication, or division,
as well as powers or roots.
Using the Order of Operations, p. 270

1. Perform operations within grouping symbols
2. Evaluate exponential expressions
3. Multiply and divide in order that they occur,
   from left to right
4. Add and subtract in order that they occur, from
   left to right
Vocabulary of Algebraic Expressions, p. 272

Terms- parts of an algebraic expression that are
separated by addition

Coefficient- the numerical part of a term

Constant term- a term that consists of just a number

Like terms- terms that have the same variables with
the same exponents
Properties of real numbers, p. 273
Let a, b, c be real numbers.
Commutativity: a + b = b + a
                 ab = ba
Associativity:   (a + b) + c = a + (b + c)
                 (ab) c = a (bc)
Distributive:    a(b + c) = ab + ac
                 (a + b) c = ac + bc
Rectangular coordinate system, or
                   Cartesian plane, p. 58
                     y-axis
Quadrant II      3                Quadrant I

                 2

                 1            Origin
                                                   x-axis
-4 -3    -2    -1             1    2    3      4
                 -1
Quadrant III    -2                Quadrant IV
                        y-axis
                    3                ( 1.2 , 2.9 )
( -3 , 2 )
                    2

                    1                                -3
                                                          x-axis
  -4 -3      -2   -1             1      2      3     4
                    -1                               ( 4, -1 )
                   -2
 The Graph of an Equation p. 337
Example : Use solution points to sketch the graph
 of the equation y = –2x with -3 < x < 3.
    Input           Output           Ordered Pair
      x           y = – 2x             ( x, y )
   x = –1,        y = – 2(–1 )   = 2 ( –1, 2)
   x = 0,         y = – 2( 0 )   = 0 ( 0, 0)
   x = 1,         y = – 2( 1 )   = – 2 ( 1, – 2 )
   x = 2,         y = – 2( 2 )   = – 4 ( 2, – 4 )
   x    -1    0      1     2
   y    2     0       –2   –4
 y
                    x     -1     0      1     2
                    y     2      0      –2    –4

                 x ( – 1, 2), ( 0, 0), ( 1, –2),( 2,–4)


                   Refer to p. 336 for ‘Graphing
                   in the Cartesian Plane’
Are these the only ordered pairs or solution points
 for the equation     y = –2x ?
Definitions                         y
Equation in two variables- an
  expression that expresses a
  relationship between two
  quantities.                                     x
Example : y = –2x
Solution- an ordered pair (a, b)
  such that if a is substituted
  for x and b is substituted for
  y in an equation, then the
  equation is true.
Example : ( – 1, 2), ( 0, 0), ( 1, –2), ( 2,–4)
 HOMEWORK
EXERCISES p. 65-66 # 1 – 65 alternate odd

CRITICAL THINKING p. 66 # 79, 80, 81

READ p.60 – 65 Set Operations and Venn Diagrams with
three sets

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HOMEWORK

Work p. 277 #1-4, 31-56 alt. odd,61-76 alt. odd, 92
     p. 343 # 1-20, 23-28 odd
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