Discrete Mathematics Questions and Answers

Discrete Mathematics Question Bank with Answer:
Discrete maths are maintained as a part of mathematics subject, which is essential for any beginner of studies. Discrete maths cover the topic like number system, element of set theory, algebraic equation relation and functions,Probability, graph theory, and matrix. The question bank is prepared based on the availability  and application of math topic. Required number of questions are given with key answers. By practicing Discrete mathematics question and answers makes the learner easy and at the same time enjoy towards the subject.

      1. Find the value of 5.123x10-2 + 6.042x10-2

         Solution: 5.123 + 6.042 = 11.165x10-2
                        the value can be divided by 10 which equals to 1.1165x10-1

       2. Insert the missing number 5,20,10,_,20,80

         Solution: 5,20,10,_,20,80
                       Here first digit is multiplied by 4,for the obtained number (second digit) divided by 2,these is how the series follows.
                         5 x 4 = 20
                       20 ÷ 2 = 10
                       10 x 4 = 40
                       40 ÷ 2 = 20
                       20 x 4 = 80
                       the missing number is 40.

       3. Evaluate 7P5 using formula

          Solution: Formula for number of permutation = nPr = $\frac{n!}{\left ( n-r \right )!}$
                         when n= 7 and r = 5, assign the value in the given formula.

                         7P5 = $\frac{7!}{\left ( 7-5 \right )!}=\frac{7!}{(2)!}=\frac{7*6*5*4*3*2*1}{2*1}$ = 7*6*5*4*3 = 2520

       4. Find the number of combinations of the letter of the word “KEYBOARD” when 5 letter is taken at a time.

          Solution: The word “KEYBOARD” has 8   different letters, when 5 letter are taken at a time

                         The number of combination = ncr = $\frac{n!}{\left ( n-r \right )!r!}$
                         here n = 8 r = 5             nCr = $\frac{8!}{\left ( 8-4 \right )!4!}$
                                                                  = $\frac{8!}{(4)!4!}=\frac{8*7*6*5*4*3*2*1}{(4*3*2*1)4*3*2*1}$ = 70

        5. Find the value of n when the first term of the series is 10, their common difference is 3 and the nth term Tn = 64

Solution: Given the first term a = 10, d = 3, Tn = 64
                         The general form the series is Tn = a +(n - 1)d
                         assign the value of the term here
                         Tn = a + (n - 1)d
                         64 = 10 + (n-1)3
                         64 = 10 + 3n -3
                         64 = 7 + 3n   (add -7 on side of the equation)
                         64 - 7 = 7 + 3n - 7
                         57 = 3n
                         $\frac{57}{3}$ = n
                         19 = n

          6. Find the sum of the series of geometric progression term 3+6+12+.......to 10 terms

          Solution: Given a = 2,  n = 10
 r = $\frac{T_{2}}{T_{1}}=\frac{6}{3}$ = 2

   = $\frac{T_{3}}{T_{2}}=\frac{12}{6}$ = 2 

                         since r is greater than 1 we have sum of series of term formula  Sn = $\frac{a\left ( r^{n}-1 \right )}{\left ( r-1 \right )}$

                         S10 = $\frac{2\left ( 2^{10}-1 \right )}{\left ( 2-1 \right )}$

                         S10 = $\frac{2\left ( 1024-1 \right )}{\left ( 1 \right )}$

                         S10 = 2 (1023)
                         S10 = 2046

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The invention and ideas of many mathematicians and scientists led to the development of the computer, which today is used for mathematical teaching purposes in the kindergarten to college level classrooms. With its ability to process vast amounts of facts and figures and to solve problems at extremely high speeds, the computer is a valuable asset to solve the complex math-laden research problems of the sciences as well as problems in business and industry. Major applications of computers in the mathematical sciences include their use in mathematical biology, where math is applied to a discipline such as medicine, making use of laboratory animal experiments as surrogates for a human biological system. Mathematical computer programs take the data drawn from the animal study and extrapolate it to fit the human system. Then, mathematical theory answers the question of how far these data can be transformed yet still preserve similarity between species. Mathematical ecology tries to understand the patterns of nature as society increasingly faces shortages in energy and depletion of its limited resources. Computers can also be programmed to develop premium tables for life insurance companies, to examine the likely effects of air pollution on forest productivity, and to simulate mathematical model outcomes that are used to predict areas of disease outbreaks. Mathematical geography computer programs model flows of goods, people, and ideas over space so that commodity exchange, transportation, and population migration patterns can be studied. Large-scale computers are used in mathematical physics to solve equations that were previously intractable, and for problems involving a third dimension, numerous computer graphics packages display three-dimensional spatial surfaces. A byproduct of the advent of computers is the ability to use this tool to investigate nonlinear methods. As a result, the stability of our solar system has been checked for millions of years to come. In the information age, information needs to be stored, processed, and retrieved in various forms. The field of cryptography is loaded with computer science and mathematics complementing each other to ensure the confidentiality of information transmitted over telephone lines and computer networks. Encoding and decoding operations are computationally intense. Once a message is coded, its security may hinge on the inability of an intruder to solve the mathematical riddle of finding the prime factors of a large number. Economical encoding is required in high-resolution television because of the enormous amount of information. Data compression techniques are initially mathematical concepts before becoming electromagnetic signals that emerge as a picture on the TV screen. Mathematical application software routines that solve equations, perform computations, or analyze experimental data are often found in area-specific subroutine libraries which are written most often in Fortran or C. In order to minimize inconsistencies across different computers, the Institute of Electrical and Electronics Engineers (IEEE) standard is met to govern the precision of numbers with decimal positions. The basic configuration of mathematics learning in the classroom is the usage of stand-alone personal computers or shared software on networked microcomputers. The computer is valued for its ability to aid students to make connections between the verbal word problem, its symbolic form such as a function, and its graphic form. These multiple representations usually appear simultaneously on the computer screen. For home and school use, public-domain mathematical software and shareware are readily available on the Internet and there is a gamut of proprietary software written that spans the breadth and depth of the mathematical branches (arithmetic, algebra, geometry, trigonometry, elementary functions, calculus, numerical analysis, numerical partial differential equations, number theory, modern algebra, probability and statistics, modeling, complex variables, etc.). Often software is developed for a definitive mathematical maturity level. In lieu of graphics packages, spreadsheets are useful for plotting data and are most useful when teaching arithmetic and geometric progressions. Mathematics, the science of patterns, is a way of looking at the world in terms of entities that do not exist in the physical world (the numbers, points, lines and planes, functions, geometric figures——all pure abstractions of the mind) so the mathematician looks to the mathematical proof to explain the physical world. Several attempts have been made to develop theorem-proving technology on computers. However, most of these systems are far too advanced for high school use. Nevertheless, the non-mathematician, with the use of computer graphics, can appreciate the sets of Gaston Julia and Benoit B. Mandelbrot for their artistic beauty. To conclude, an intriguing application of mathematics to the computer world lies at the heart of the computer itself, its microprocessor. This chip is essentially a complex array of patterns of propositional logic (p and q, p or q, p implies q, not p, etc.) etched into silicon . see also Data Visualization; Decision Support Systems; Interactive Systems; Physics. Patricia S. Wehman Devlin, Keith. Mathematics: The Science of Patterns. New York: Scientific American Library, 1997. Sangalli, Arturo. The Importance of Being Fuzzy and Other Insights from the Border between Math and Computers. Princeton, NJ: Princeton University Press, 1998.

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Question:Hello, I need to solve the discrete mathematics problem, proposition for p and q ................._____......_____ ........................_............_ p <=> q ( p q ) ( q p ) Thanks for your help in advance, B/R. Hey! I would appricate if someone help me :( B/R

Answers:p <=> q ( p q ) ( q p ) p <=> q p q q p p <=> q p q

Question:Ms Pezzulo teaches geometry and then biology to a class of 12 advanced students in a classroom that has only 12 desks. In how many ways can she assign the students to these desks so that (a)no student is seated at the same desk for both classes? (b)there are exactly six students each of whom occupies the same desk for both classes?

Answers:The only feasible way for one to occupy a desk without being "seated" is to stand on the desk. So in the first class session, Group A (consisting of 6 students) sits in their respective chairs and so does Group B (6 students). In session 2 Group A stands in their same desk instead of sitting ang Group B switches seats with one another, like musical chairs. Since this arrangement only involves the movement of Group B, there are 216 (6 students times 6 chairs times 6 chairs) possible seating arrangments for Group B for every 1 seating arrangement for Group A. There are 36 possible seating arrangements for Group A (6 students times 6 chairs). So we have 216*36=7776 So Ms Pezzulo has a whopping 7776 seating arrangment options for our single sit -down/stand-up solution. If you want to be technical with it, you should multilply this solution by thenumber of possible bodily positions one could use to occupy a desk without actually putting one's bottom in the seat. LOL. Have at it! I'm going to bed. X-) ZZZZZZZZZ

Question:I am having some difficulty in my Discrete Mathematics course. I don't want to post the question up here just to get the answer. I am looking for help on understanding the process of how to solve the problem so that I can finish the assignment. Here is the problem: Show that 6 divides (a^3 - a) for all integer numbers a>=2. (Hint: One of 3 sequential integers is divisible by 3). I tried writing out the first few terms but I am still lost on how to attack this problem. Are any websites that can explain discrete mathematics in a simpler manner? Also this question if from the professor himself (he decides to give us problems that are not in the book....so the book is little help)

Answers:The key is noticing that: a^3 a = a(a^2 1) = = a(a 1)(a + 1) But a, a 1 and a + 1 are three consecutive integers, so at least one is even, which means that 2|(a^3 a). Now, if you divide these three integers by 3, you'll see that at least one of the reaminders must be 0, which is to say that the corresponding integer is divisable by 3, so 3|(a^3 a). But gcd(2,3) = 1 so, as a^3 a is divisible by both 2 and 3, it must be divisible by their product, 6.

Question:is there anywhere i can get the even answers for this book?please help my final exam is tomorrow

Answers:If you post this question in the Science and Mathematics category someone browsing there may be able to help you with it.

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