## INTRODUCTION TO SET

We often deal with a group or a collection of objects,  such as a collection of books, a collection of English alphabets, a group of students, a list of states in a country, a collection of coins, etc. Set may be considered as a mathematical way of representing a collection or a group of objects.

Definition of Set :

A set is a collection of well defined objects. The objects of a set are called elements or members of the set.

The main property of a set is that it is well defined. This means that given any object, it must be clear whether that object is a member (element) of the set or not.

Generally, sets are named with the capital letters A, B, C, etc. The elements of a set are denoted by the small letters a, b, c, etc.

Examples of Sets in Daily Life :

• Students in our class room
• Collection of animals in the world
• Collection of fruits
• Collection of vegetables

Question 1 :

A collection of all natural numbers less than 50.

If forms a set. The set will have the following elements.

A = {1, 2, 3, 4, 5, ...................50}

Question 2 :

A collection of good hockey players in America

If doesn't form a set. Because the term "Good player" is vague and it is not well defined.

However a collection of players of hockey is a set.

Question 3 :

A collection of all girls in our class.

If forms a set. The elements of the above set is the names of those girls in the class.

Question 4 :

A collection of prime numbers less than 30

If forms a set.  The set will have the following elements.

A = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }

Question 5 :

A collection of ten most talented mathematics teachers.

If doesn't form a set. Because the term "Most talented" is vague and it is not well defined.

However a collection of players of hockey is a set.

In this chapter we will have frequent interaction with some sets, so we reserve some letters for these sets as listed below. :

N  :  The set of natural numbers

Z  :  The set of integers

Z+  :  The set of all positive integers

Q  :  The set of all rational numbers

Q+  :  The set of all positive rational numbers

R+  :  The set of all real numbers

R+  :  The set of all positive real numbers

C  :  The set of all complex numbers

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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6