Unit 1 : Sets (Recalling the basics)

Unit1: Sets

Before we get started with the lesson, let us first recall what is basic to know for this unit of sets.

Recalling the basics
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Objectives:

Ø  Commutative and Associative property of union and intersection of sets.

Ø  Verification of commutative and associative property of union and intersection of sets.

Ø  Distributive property of sets.

Ø  De Morgan’s law.

Ø  n (A) + n (B) = n (A ⋃ B) + n (A ⋂ B).

Ø  Venn Diagrams.

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                              We have already learnt about the sets in the previous classes, what a set is?                     Different types of sets and different operations of sets. In this chapter we will learn few                 more operations with sets. Let us again recall few important terms and definitions used                 in this unit.

       Introduction to SETs:

       What is a set?

       Set is a collection of elements with a common property. Each element/member of a set is              separated by a comma, and then put it all under a pair of curly brackets.

Set of whole numbers: {0, 1, 2, 3, ...}

      The three dots in the end of set elements “...” are called an ellipsis, and mean "continue on".          But sometimes the "..." can be used in the middle to save writing long lists.

The set of letters:

{a, b, c, ..., x, y, z}

      Sets are represented by the Capital Letters and the elements are represented by Small                    letters.

A = {a, e, i, o, u}

    Universal Set:

       It's a set that contains everything. Well, not exactly everything. Everything that is relevant         to our question.

    Operations of Sets

       Let us write the set of friends who pay cricket and set of friends who play hockey.

        Cricket = {Rahul, Aamir, Yash, Sunny, Vinay}
        Hockey= {Kishore, Yash, Vinay, Vinod, Sohail}

Union of Sets:

       Now we can list the friends that play Cricket or Hockey
      This is called a "Union" of sets and has the special symbol ⋃:

       

Cricket ⋃ Hockey = {Rahul, Aamir, Sunny, Yash, Vinay, Kishore, Vinod, Sohail}

    Intersection of Sets

       “Intersection” is when you have in both the sets.

        Symbol for Intersection is an upside down "U" like this: ∩

       Cricket ⋂ Hockey = {Yash, Vinay}

         Subtraction of Sets

         We can also subtract one set from another.

                                      For example, we take people who play Cricket but not Hockey, which is                     Rahul, Aamir and Sunny.

          We write it down as:

          Cricket – Hockey = {Rahul, Aamir, Sunny} or

          Cricket /Hockey = {Rahul, Aamir, Sunny}

        Complement of Sets

        It is a special way of saying, “Everything that is not”.

        It is obtained by subtracting the elements of a set from the Universal Set.

Further topics will be discussed in the next post. Please keep your self updated for all other discussion of the topic.