Skip to main content

Discrete mathematics

            It's about Discrete mathematics in this book  #Anthony Croft, Engineering Mathematices, 5e (2017) 



So i will choose exercise 5.2 #7 #8 #9  to slow everyone:

 7. The sets A, B and C are given by A = {1, 3, 5, 7, 9},
B = {0, 2, 4, 6} and C = {1, 5, 9} and the universal

set, E = {0,1, 2, . . . ,9}.
(a) Represent the sets on a Venn diagram.
(b) State A ∪ B.
(c) State B ∩ C.
(d) State E ∩ C.
(e) State not A.
(f) State not B ∩not C.
(g) State not (B ∪C).
  • Ans : 




 a) Represent the sets on a Venn diagram :

 The set containing all the numbers of interest is called the
universal set, E. E is represented by the rectangular region. Sets A , B and C are represented by the interiors of the circles and it is evident that 1,  3,  5,  7 and 9 are members of A while 0,
2,  4,  and 6 are members of B that 1,  5  and  9 are members of C.  The elements 1 ,  5 and 9 are common to both sets.



 b) State A ∪ B :

 The set which contains all the elements of A and those of B is

called the union of A and B, written as

                  b)   {0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9}
c) State B ∩ C :

 the set B ∩ C has no elements we say the sets B and C are disjoint and write B ∩ C = empty set.


d) State E ∩ C :

 The set which contains the elements common to both E and  C is called the intersection of E and C, written as

                    d)   {1 ,  5  ,  9}

 e) State not A :

 The set of members of E that are not in A is called the complement of A : 

                   e)     {0 , 2 , 4 , 6 , 8}

 f) State not B ∩  not C : 

 The set of members of E that are not in B  and not in C is called the complement of B and C : 

                    f)      {3 , 7 , 8}

 g) State not (B ∪C) :

 The set which contains all the elements of not A and those of not B is called the union of not A and not B, written as

                    g)      {3 , 7 . 8}

 8.Use Venn diagrams to illustrate the following for
general sets C and D:

 (a) C ∩D              (b) C ∪ D                (c) C ∩ not_D
(d) not (C ∪D)            (e) not (C ∩D)
Ans :

 a) C ∩D :

 The set which contains the elements common to both C and  D is called the intersection of C and D, written as

b) C ∪ D :

 The set which contains all the elements of C and those of D is

called the union of C and D, written as

c) C ∩ not_D :

 The set which contains the elements common to both C and  D is called the intersection of C and D, written as


d) not (C ∪D) :

e) not (C ∩D) :


9.By drawing Venn diagrams verify De Morgan’s laws


 A1 . not(A ∩B) =notA ∪ notB



The set which contains all the elements of A and those of B is called the union of A and B, but Not (A  and B) 
the set which not contains all the elements of A and those of B.

                                                                         



The set which contains all the elements of A and those of B is called the union of A and B, but Not (A  and B) 
the set which not contains all the elements of A and those of B.



So this answer : 



A2 .  not (A ∪B)  = notA ∩notB  
         
              not (A ∪B)   

                                                            



               notA ∩notB





                                                       


So not (A ∪B)  = notA ∩notB 













Labels:

Comments

Post a Comment

Popular posts from this blog

Lab 2 , 3 , 4 Method math in java

Class Teedcalculator: /*  * To change this license header, choose License Headers in Project Properties.  * To change this template file, choose Tools | Templates  * and open the template in the editor.  */ package teedcalculator; import static teedcalculator.Oparetor.tand;// to access all static Tand of a class import static teedcalculator.Oparetor.tan;// to access all static Tan of a class import static teedcalculator.Oparetor.cost;// to access all static Cost of a class import static teedcalculator.Oparetor.cosd;// to access all static Cosd of a class import static teedcalculator.Oparetor.degree2;// to access all static Degree of a class import static teedcalculator.Oparetor.divide;// to access all static divide of a class import static teedcalculator.Oparetor.minus;// to access all static minus of a class import static teedcalculator.Oparetor.modulo;// to access all static modulo of a class import static teedcalculator.Oparetor.multiply;// to acce...
Post a Comment
Read more

Barometric pressure sensor with Arduino

Hardware Required - Arduino or Genuino board - SCP1000 Pressure Sensor Breakout Board - hook-up wires  Procedure  Follow the circuit diagram and make the connections as shown in the image given below. Arduino Code /******* All the resources for this project:   https://lihuo.blogspot.com *******/ The code below starts out by setting the SCP1000 's configuration registers in the setup() . In the main loop, it sets the sensor to read in high resolution mode, meaning that it will return a 19-bit value, for the pressure reading, and 16 bits for the temperature. The actual reading in degrees Celsius is the 16-bit result divided by 20.   Then it reads the temperature's two bytes. Once it's got the temperature, it reads the pressure in two parts. First it reads the highest three bits, then the lower 16 bits. It combines these two into one single long integer by bit shifting the high bits then using a bitwise OR to combine them...
2 comments
Read more

Software Arduino IDE

Arduino is an open source computer hardware and software company, project, and user community that designs and manufactures single-board microcontrollers and microcontroller kits for building digital devices and interactive objects that can sense and control objects in the physical world. A program for Arduino hardware may be written in any programming language with compilers that produce binary machine code for the target processor. Atmel provides a development environment for their 8-bit AVR and 32-bit ARM Cortex-M based microcontrollers: AVR Studio (older) and Atmel Studio (newer). IDE The Arduino integrated development environment (IDE) is a cross-platform application (for Windows, macOS, Linux) that is written in the programming language Java. It originated from the IDE for the languages Processing and Wiring . It includes a code editor with features such as text cutting and pasting, searching and replacing text, automatic indenting, brace matching, and syntax highl...
Post a Comment
Read more