Essentials of Discrete Mathematics

Definition of Discrete mathematics:

The essential of discrete mathematics is significant one in computer evaluation. It give details the algorithms and theory for computer enhancement.The essential of discrete mathematics is the study of exact structure that are basically discrete relatively than nonstop. In difference to real numbers that have the possessions of varying "effortlessly", the objects are deliberate in essential of discrete mathematics  such as integers, graphs, and statements in logic do not differ smoothly in this way, but have dissimilar, separated values.

Discrete Mathematics Topics

Theoretical computer science:

Calculating area for essential of discrete mathematics is incorporated in theoretical computer science. If we desire to study the result of mathematical computation, use this theoretical science. Model computer systems are utilizing the method algebra.

Information theory:

Quantification of information is anxious with information theory. In this, coding theory is used since it sketch the chart strongly and honest data transmission.

Logic:

Valid reason and assumption philosophy are measured by logic. Truth tables are use in normal logic.

Graph theory:

Graphs and networks are calculated by graph theory. It is used for observe the problem result.

Probability:

The actions are significant the countable samples and dense with discrete probability theory.

Algebra:

Boolean algebra along with relational algebra use the discrete examples. Topology, geometry, calculus, game theory and numeral theory also concern of  the essential of discrete mathematics.

Examples of Discrete Mathematics
Question: 1

Find n.

i) (n+2)!=12*11(n!)

Answer:

(n+2) (n+1)n!=12*11(n!)

(n+2)(n+1)=12*11

`n^2` +3n-130=0

(n-10)(n+13)=0

n=10 or n= -13

n=10(n cannot be negative)

ii) `1/(7!) +1/(8!) = n/(9!)`

`1/(7!) + 1/(8!) = n/(9.8(7!))`

Answer:

`1 + 1/8 = n/(9.8)`

`9/8 = n/(72)`

`n= (9 * 72)/8 = 81`

n =  81

Question: 2

A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees?

Answer:

Here, there are two events E1 and E2.
E1 = Selection of one cotton saree from 8 cotton sarees.
E2 = Selection of one polyster saree from 11 polyster sarees.
E1 = 8 ways E2 = 11 ways

Question 3

i)`20!+(19!)/(18!)` ii)`30!-(28!)/(26!)` iii) `8!+(6!)/(7!)`

Answer

i)                    `20!+(19!)/(18!)= 19!(20+1)/(18!)=19*(18!)*21/(18!)=19*21=399`
ii)                  `(30!-28!)/(26!)=28!((30*29)-1)/(26!)=28*27*869=656964`
iii)                `(8!+6!)/(7!)=6!(8*7+1)/(7!)=57/7`