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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
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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
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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
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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
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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
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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
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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
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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