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 Discrete Maths (DM) - Assignment No. 2 Q. 1: How many friends must you have to guarantee that atleast five of them will have birthday in the same month.  Q. 2: Solve the recurrence relation a. a r+2 -a r+1 -6a r =4. b. a n =6a n-1 +11a n-2 -6a n-3 given a 0 =20, a 1 =5 and a 2 =15. Q. 3: a. Consider Group G={1,2,3,4,5,6) under multiplication modulo 7 find multiplication modulo 7. b. Let G be the set of rational numbers other than 1. Lets define an operation * on G by a*b=a+b-ab for all a,b c. Prove that (G,*) is a group. Q. 4: Let H be a parity check matrix, determine the group code e H : B3->B 6 . H =  1 0 0           0 1 1           1 1 1           1 0 0           0 1 0           0 0 1 Q. 5: Prove that a connected graph G is an Eulerian graph if and only if all vertices of G are of even degree. Q. 6: What is Travelling Salesperson Problem? How is it solved? Solution for DM assignment 2 is given below. https://drive.google.com/file/d/1POeHvcWZ4DxOY-7m6qKdfLgsByLAu1oh/view?usp=

Discrete Maths (DM) - Assignment 1  Q. 1: Prove by mathematical induction 1 3 + 2 3 + …+ n 3 = [n 2 (n + 1) 2 ] / 4.  Q. 2: Use the laws of logic to show that the following proposition is tautology. ((p  q) ˄ ̴ q)  ̴ p) Q. 3: Out of 250 candidates who failed in an examination, it was revealed that 128 failed in mathematics, 87 in physics, 134 in mechanics, 31 failed in mathematics and physics, 54 failed in mechanics and mathematics, 30 failed mechanics and physics. Find how many candidates failed - In all three subjects - In mathematics but not in physics - In mechanics but not in maths - In physics but not in mechanics nor in maths. Draw a venn diagram. Q. 4: Let m be a positive integer greater than 1. Show that the relation is an equivalence relation. R = {(a,b) | a ≡ (b mod m). Q. 5: Show that in a distributive lattice (A, ≤) if a ˄ x = a ˄ y and if a ˅ x = a ˅ y then x = y. Q. 6: Determine the matrix of the partial order of divisibility on the set A. Draw Hasse diagram of the pos

  AIM: To implement ripple carry adder Objectives: To implement n-bit ripple carry adder using virtual lab. CO’s to be achieved: 1 ( Design and simulate different digital circuits) PO’s to be achieved:   PO1, PO2, PO3, PO10 APPARATUS REQUIRED: Power supply , Breadboard, virtual simulator COMPONENTS: ICs 7486,7408, 7432 and trainer kit THEORY: Full adder : The adder circuit is capable of adding the content of two registers. It must include provision for handling carries as well as an addend and augends bits. So there must be three inputs to each stage of a multi digit adder, except the stage for the least significant bits. One for each input from the numbers being added, one for any carry that might have been generated or propagated by the previous stage. Ripple Carry Adder-   Ripple Carry Adder is a combinational logic circuit. It is used for the purpose of adding two n-bit binary numbers. It requires n full adders in its circuit for adding two n-bit binary numbers. It is also known