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MATH 1033 Chapter 1

A.Evaluating Algebraic Expressions


Def: A letter representing an arbitrary number is called a variable.


Def: An algebraic expression is formed by numbers and variables connected by arithmetic operations.


Ex :


Def: To evaluate an expression , one substitutes a numeric value for each variable in an expression .


Ex : When t=5.2,8443t evaluates to 49,903.6


1. Evaluate the area (A=bh) of a parallelogram with base 10 centimeters and 8.2 centimeter height.


2. Evaluate the area (A=(1/2)bh) of a triangle with base and height of 3.5cm and 8cm respectively.


3. Evaluate 3x-y,x=15,y=4


4. Evaluate 2p-q,p=17,q=3

B. Subsets of the Real Numbers

Def : The empty, or null, set is the set of no elements. It is denoted by either or {}.
Note : The symbol " ∈" is read "is an element of." Likewise " " is read "is not an element of."
Def : The subsets of the real numbers are :

Natural{1,2,3,4...}

Whole {0,1,2,3,4,...}

Integers {...,-2,-1,0,1,2,...}

Rational {(p/q):p,q∈}

Irrational {} Note: The symbol is rarely used.

Real {x:x has an infinite decimal expansion}
For a more complete definition of the real numbers, see:
Courant, Richard, and Robbins, Herbert : " What is Mathematics ?"
Chapters 1,2,Oxford, New York (1941)

Complex {z=a+bi,a and b,i is the imaginary unit, i2=-1"}
We will study the complex numbers in detail later on.

Def :The union, denoted ∪, of two sets is the set of all elements of either of the the individual sets.

Ex :{1,2,3}∪{3,4,5}=

Def :The intersection, denoted  ∩ , of two sets is the set of all elements in each of the individual sets.

Ex :{1,2,3}∩{3,4,5}=

List out the elements in each of the following sets :

5.{x:x∈ and B is greater than 100}

6.{x:x is a whole number between 0 than 6}

7.{x:x∈ and x is no greater than 20}

Determine wiether each statement is true or false :

8. 3∈

9. 7∈{1,2,3}

Note : A number expressed as a fraction is rational . However, a terminating or repeating decimal is also
a rational number .

10.

Def : The symbol " ⊆ "denotes a proper subset. That is, every element in the left hand set is in the
right hand set, and the sets may be equal (having exactly the same elements).

Ex:

Def : If the two sets are not equal, one may use the symbol " ⊂ ".

5. Insert the appropriate symbol of those given to make the statement true.

(Proper subset or not a proper subset.)
(Proper subset or not a proper subset.)

Def : The absolute value of a number + is :

6.Evaluate each  absolute value.

Def : The opposite ( addative inverse ) of a number a is -a.
Def : The reciprocal (multiplicative inverse) of a number a is (1/a).

7. Find the inverses of each number.

Addition  Multiplication

5.4

-3/5

18

-9.6

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