SET Identities

8/11/2019 SET Identities

1/21

SET Identities


2/21


3/21

SET Application

Inclusion- Exclusion Principle

Let A and B be any two finite sets. Then

= + | |


4/21


5/21

Set of Real Numbers


6/21

The Real Number System

this system consists of the set R of elementscalled real numbers and two operations addition

and multiplication.


7/21

Set of Positive

Integers (Z+, N)

{1,2,3,4}

Set of Negative

Integers (Z-)

{..-,3,-2,-1}

Set of Whole

Numbers (W)

{0,1,2,3,}

Set of

Integers (Z) --{-3,-2,-

1,0,1,2,3,}

Set of Rational

Numbers (Q)-- {x|x

is a number which

can be expreseed in

the form p/q, where

p and q are both

integers and q0}

Set of irrational

Number (Qc)--- ) {x|x

is a number which

cannot be expressed

as a quotient of two

integers


8/21

Rational Numbers

Rational Numberis either a terminating ornonterminating but repeating decimal.

Example:Terminating decimals

3/8 =0.375 b. -7/2 = -3.5

Non-terminating but repeating decimal.

18/11 = 1.636363 = 1.63 b.-442/45 = -9.8222 =-9.82


9/21

Irrational Numbers

is a non-repeating , nonterminating decimal

Example:

7= 2.65575513 = 2.6558 (dec.. expansioncontinues but w/o any pattern)

= 3.141592654


10/21

An integer is said to be EVENif its is divided by2, that is, if it can be expressed in the form 2n for

some integer n.

An integer is said to be ODDif it can be

expressed in the form of 2n+1 for some integer n.


11/21

REAL NUMBER LINE

Real axis having a one to one correspondenceexists between the set R and the set of points onan axis.

> 0 < 0


12/21

Basic Properties of Real

Numbers


13/21


14/21


15/21

Two important consequences of the substitution

property are the following:

If a = b, then a+ c= b+c

If a = b, then ac=bc

The converses of these two rules are called the

Cancellation Laws for addition and multiplication,

respectively.

If a+c =b+c, then a=b

If ac=bc, then a=b, c0.


16/21


17/21


18/21

Operations on Signed Numbers

Addition of Signed NumbersTo add real numbers with like signs, get the sum of theirabsolute values and prefix the common sign.

Subtraction of Signed Numbers

To subtract two signed numbers, change the sign of thesubtrahend and proceed to algebraic addition.

Multiplication of Signed Numbers

The product of two or more signed numbers is either (+)or (-) depending on whether the number of negativefactors is even or odd, respectively.


19/21

nth Power of Real NumbersFor any positive integer, we define a=bnas an nth

power of b.

Square roots and Cube Roots of RealNumbers

We use the relation, a = bn

The square root of a , denoted by , is defined as

= if and only if a=b2

The cube root of a, denoted by 3 , is defined as =

3 =


20/21


21/21

SET Identities

Documents