EECS 70
Spring 2016
Discrete Mathematics and Probability Theory
Satish Rao, Jean Walrand
Discussion
5B
1. Repeated Squaring Compute 3383 (mod 7). (Via repeated squaring!)
2. Modular Potpourri
(a) Evaluate 496 (mod 5)
(b) Prove or Disprove: There exists so
CS 70
Discrete Mathematics and Probability Theory
Spring 2016
Rao and Walrand
Discussion 4A
1. Recursive Calls Calculate the greatest common divisor (gcd) of the following pairs of numbers using the
Euclidean algorithm.
[Hasty refresher: starting with a p
CS 70
Discrete Mathematics and Probability Theory
Fall 2016
Rao and Walrand
Discussion 1A
1. Set Operations
N denotes the set of all natural numbers: cfw_0, 1, 2, 3, ..
Z denotes the set of all integer numbers: cfw_. . . , 2, 1, 0, 1, 2, . . ..
Q denot
CS 70
Discrete Mathematics and Probability Theory
Spring 2016
Rao and Walrand
Discussion 3A
1. Odd Degree Vertices
Claim: Let G = (V, E) be an undirected graph. The number of vertices of G that have odd degree is even.
Prove the claim above using:
(i) Ind
CS 70
Discrete Mathematics and Probability Theory
Spring 2016
Rao and Walrand
Discussion 2A
1. Power Inequality
Use induction to prove that for all integers n 1, 2n + 3n 5n .
2. Triangle Inequality
Recall the triangle inequality, which states that for rea