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

Which of the following collection are sets ? Justify your answer.

**Question 1 :**

A collection of all natural numbers less than 50.

**Answer :**

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

**Answer :**

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.

**Answer :**

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

**Answer :**

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.

**Answer :**

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 **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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**

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**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 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**

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**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**