Sets

---A set is a collection of objects. Sets are denoted by A, B, C… ,

---The objects in the set are called the elements of the set. The elements are

denoted by a, b, c… ,

Hessah Wael Hiji Al-Shemmary

Sets

---If a is an element on a set A we write a A if a is not in A we write a A.

---The elements in a set X can be written in the form X.}....... ,....... ,.......{ =

---If X has no elements we write X = {} or and call it the empty set.

Hessah Wael Hiji Al-Shemmary

Sets

---XY denotes the intersection of two sets X and Y and it is the set which

contains all the elements belonging to X and Y. ---XY denotes the union of two sets X and Y and

it is the set which contains all the elements belonging to X or to Y. ---Sets can be finite, infinite or empty.

Hessah Wael Hiji Al-Shemmary

Exercises :

(1 )Identify the following sets (a ) = } {S students that can fly

(b ) B the set of positive integers less than 3or equal to.

(2 )If A = {1,3,5,7,9}, B = {1,2,3,4,5} and C ={5,6,7,8,9} find

i) A ∩ B ii) A U C iii) A U B U C iv) A ∩ B ∩ C

Hessah Wael Hiji Al-Shemmary

Operations on Real Numbers:

---The set of Real Numbers is denoted by the symbol R :

---The operations on real number are addition, subtraction, multiplication and

division.

Hessah Wael Hiji Al-Shemmary

Exercises :

(1 )Add 5 to 6.(2 )Subtract 3 from 7.

(3 )Multiply 3 by 8.(4 )Divide 30 by 10.

(5 )Multiply 20 by 5 and then subtract 43 ..

Hessah Wael Hiji Al-Shemmary

The set of Real numbers has important subsets:

The natural numbers: 1, 2, 3, … is denoted by N The integers: …, -2, -1, 0, 1, 2, ... is denoted by Z

The rational numbers: the real numbers of the form a/b where a, b are integers and b # 0 is

denoted by Q .

Hessah Wael Hiji Al-Shemmary

Excercises:

Circle the right answer:(1 )The real number 3/5 is

( a ) ) ( an integer b not a rational number ( c )a natural number (d) not an integer

(2 )If you add an integer to a rational number you always get:( a )an integer (b) a rational number

( c ) ) ( a natural number d a negative realnumber.

(3 )Two integers, the ratio between them is 3 : 7 and if substracted 5 from each term, the ratio between each of them becomes 1 : 3. Find

the two numbers?

Hessah Wael Hiji Al-Shemmary