Discrete Math: Logic Problems, Truth Table and Rules of Inference

Please see the attached file for the fully formatted problems. 1. Construct the truth table for the compound proposition: [p (q r)] (r p) p q r ------------------------------------------------------------- T T T T T F T F T T F F F T T F T F F F T F F F 2. What is the negation of the quantified statement: For every integer, x, there is an integer, y, such that x + y = 0. 3. Use the rules of inference to deduce the following conclusion from the following set of premises. Premises: p r r q p s t ~q ~r ᠑... click for more

Graphs and Digraphs : Edge-Connectivity

If G is a graph of order n>=2 such that for all distinct nonadjacent vertices u and v, d(u)+d(v)>=n-1, then the edge-connectivity k1(G)=Deta(G), where Deta(G) is the least degree of G.

Discrete Math: Logic and Directed Graphs

Please see the attached file for the fully formatted problems. 1. Circle T for True or F for False as they apply to the following statements: T F Every compound is either a tautology or a contradiction. T F Integers are Rational. T F The empty set has no subsets. T F Onto functions map smaller sets to bigger sets. T F Disjoint sets have non-empty intersections. T F In Logic, the Implication process is, in reality, a Disjunctive process. T F A Sequence is a Function with the inputs selected in an ordered fashion. T F Bijective functions maps sets of the same cardinality to one another. T F The converse and inverse of a conditional statement are logically equivalent. T F The neg... click for more

Problems - Discrete

1. For the function f:{1, 2, 3, 4, 5} {1, 2, 3, 4, 5} defined as: f = {(1,4), (2,5), (3,1), (4,2), (5,3)}, (a) find f 1; (b) find f o f o f o f o f . 2. Which of the strings,11111111, 00000000, 10010110, or 00001011, is closest in Hamming distance to 01101001? 3. Find the polynomial big-O estimate for the function: (n7log3 n + n9)(n3 + 7log n) 4. Write out the algorithm which describes the computation of: . 7i 2j +  j i = 5_ i 1 = 5_ 5. If a is an odd integer, show that a2 1 mod 8. 6. If m is a positive integer, and a and b are integers with a b mod m, show that a mod m = b mod m.

Planar Graph

Prove that the complete graph K5 is nonplanar.