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Sanjivani Rural Education Society’s Sanjivani College of Engineering, Kopargaon-423603 (An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune) NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified Department of Information Technology (UG programme NBA Accredited) Academic Year 2023-24 Semester-I Discrete Mathematics Continuous Internal Assessment [Part B ] Activity Date:- Prepare a group-wise presentation considering the following points (not limited to): Introduction, Implementation, Example (Real life), Animation, references etc. Evaluation will be based on the following criteria: 1. Content (2 Marks) 2. Team Work and Communication (2 Marks) 3. Knowledge (2 Marks) 4. Body Language (2 Marks) 5. Q & A (2 Marks) 0 Mark 1 Mark 2 Mark Not Present Average Good Time: 12 mins (Presentation)+ 3 mins (Q & A) = 15 mins Problem Definitions for each group are as follows: Group ID Problem Definitions 1 Draw the Venn Diagrams which show the relationships in complex organizations such as the European Economic Union. 2 Imagine that your great, great, … grandfather Jim had two children. Call this generation one, so that generation one contains 2 springs of Jim Each of these children has two children, so generation two will have 4 springs. Each of the four spring has 2 children, so, at 3rd generation, we have eight spring. If this sequence continues generation after generation, prove that at n generation, there will be 2n springs? [Hint Mathematical Inducation] 3 Imagine an email system that delivers emails to people who join a group. It sends emails in the following way: it sends no mail to the first person, one mail to the second person, 2 mails to the third person, and so on. What is the recurrence relation which represents the total number of emails sent when the nth person joins the group? [Hint Linear Recurrence Relation].
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4 John received 12 rare stamps as a gift from his grandfather, so he decided to start a stamp collection. From the following week onward, John added 4 new stamps to his collection each week. What is the number of stamps he will have in the nth week? [Hint Linear Recurrence Relation] 5 A box contains 12 socks of white colour and 12 socks of black colour, all unmatched. A man takes socks out at random in dark. How many minimum socks must he take out to be sure that he has at least 2 socks of the same colour? [Hint Pigeon Hole ] 6 If you draw five points on the surface of orange in a permanent marker, then there is a way to cut the orange in half so that four of the points will lie on the same hemisphere (suppose a point exactly on the cut belongs to both hemispheres).[Hint Pigeon Hole ] 7 Draw a Venn diagram for COVID-19, which give detail. 8 Start with a square piece of paper. You want to cut this square into smaller squares, leaving no waste (every piece of paper you end up with must be a square). It is possible to cut the square into 4 squares. You can also cut it into 9 squares. It turns out you can cut the square into 7 squares (although not all the same size). What other numbers of squares could you end up with? 9 You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. 10 After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. 11 Suppose n teams are participating in a football tournament where each team plays with every other team. Prove that, at any intermediate moment of the tournament, there are always two teams that have played the same number of matches. 12 Suppose the Cassiopeia constellation represents the Hasse diagram of a partial order. List the ordered pairs of the relation and determine its binary matrix. 13 Let Cancer constellation represent the Hasse diagram of a partial order relation. List the ordered pairs of the relation and find its binary matrix. Mr. C. D. Bawankar Dr. M. A. Jawale Subject Incharge HoD IT.