Engineering Needz

 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 Travel...

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 o...