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Question 1

Question 1

Question 2

Question 2

In the diagram below place the following numbers making sure you put them in their smallest set, for example 2 goes in  N which implies its then in all the others.

equation

 

 

MATH STUDIES

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Number and Algebra

Simple Set Notation

Number sets:

The following are the different number sets you will see in the IB exams:

NorN

This is the set of all the Natural numbers  { 0, 1, 2, 3, 4......}

 

ZorZ

This is the set of integers (whole numbers positive and negative);
{ ...-3, -2, -1, 0, 1, 2, 3 ...}

 

QorQ

This is the set of rational numbers, that is numbers that can be written in the form

aoverb

 

where a and beZ and bnot equal to 0

 

examples   -5, 0.5,  1over3,  100,  minus2over7 etc.

square root 2 is not a rational number.

RandR

This is the set of all real numbers from negative infinity to positive infinity. It is any number that can be put on the real number line

 

equation 1

 

 

To check if it is a real number if you enter it into your calculator and press enter it will say NON REAL answer if not real.

 

An example of a non real number is non real number

 

 

 

 

 

We can represent the above sets using a diagram:

 

 

check sets

 

 

This is an example of a Venn Diagram (See Section on Sets, logic and Probability).

 

Other useful set definitions:

Prime numbers : This is the set of all positive integers that are divisible only by itself and 1.

Hence 1 is not a prime number.

Prime numbers = { 2,3,5,7,11......}

There are mathematicians that are constantly working on finding the largest prime number

 

Factors : This is a number by which another number can be divided to give a whole number answer.

Example: Factors of 12 are {1,2,3,4,6,12}

 

Multiples : This is best explained by giving examples.

Multiples of 3 are {3, 6, 9, 12.....}

Multiples of 5 are {5, 10, 15, 20.....}

 

Set Notation

set notation

 

The following will be used to explain and give examples of the notations above.

The letter U is normally used to represent the Universal set and letters A, B and C for example, represent subsets of the universal set.

Example : Given U =example U
This is another way of writing that x is a natural number greater than 1 up to and including 15.

Hence U= {2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A= {multiples of 3} = {3, 6, 9, 12, 15}

B= {factors of 12} = {2, 3, 4, 6, 12}

C= {prime numbers} = {2, 3, 5, 7, 11, 13}

 

subsets

 

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