Discrete Math - Set Theory / Identity / Proof : X-(A∩B)=(X-A)U(X-B)

Discrete Math - Set Theory / Identity / Proof For all sets A, B, and X, Prove the "attachment" with the use of laws such as DeMorgan, distributive, etc. Union, intersection

Discrete Math - Set Theory / Identity / Proof : (B^c U (B^c - A))^c = B

Discrete Math - Set Theory / Identity / Proof For all sets A and B, Prove the "attachment" with the use of laws such as De-Morgan's , distributive, associative, etc. De Morgan's, De-Morgans

Discrete Math - Set Theory / Identity / Proof : Prove for all sets A, B and C, if A⊆C and B⊆C then AUB⊆C

Discrete Math - Set Theory / Identity / Proof Element Argument on attachment - Need a sample step by step solution. Subsets, union

Discrete Math - Set Theory / Identity / Proof : Prove for all sets A, B and C, if A⊆B then AUC⊆BUC

Discrete Math - Set Theory / Identity / Proof Element Argument on attachment - Need a sample step by step solution. Subsets, Union

Inverse Functions and Set Operations

Let f be a function from A to B. Let S and T be subsets of B. Show that: a) -1 -1 -1 f (S U T) = f (s) U f (T) b) -1 -1 -1 f (S n T) = f (S) n f ( T)

Predicates, Logical Connectives and Quantifiers

Let P(x), Q(x) and R(x) be statements "x is a clear explanation", "x is satisfactory" and "x is an excuse" respectively. Suppose that the universe of discourse for x consists of all English test. Express the following statements using quantifiers, logical connectives and P(x), Q(x) and R(x) a) All clear explanations are satis ...continues

Project Management, PERT, Combinations, Venn Diagrams, Equivalence Relations, Trees and Graphs and Algorithms

1 The table below tells the time needed for a number of tasks and which tasks precede them. Make a PERT diagram, and determine the project time and critical path. Task Time Preceding Tasks ______________________________ A 3 NONE B 5 NONE C 2 A D 4 A, B E 6 A, B F ...continues

Sets, Relations, Prim's Algorithm, State Tables and Recurrence Relations

1. Let A = {1, 2, 3, 4}, B = {3, 4, 5}, C = {1}, and D = {x: 3 < x < 10}. Are each of the following true or false? b. B ⊆ D c. ∅ ⊆ D 2. Calculate the following: a. P(8, 4) 3. Let A = {1, 2, 3, 4}, B = {1, 4, 5}, C = {3, 5, 6}, and the universal set U = {1, 2, 3, 4, 5, 6}. a. Determi ...continues

Combinatorial Techniques : What is the algorithm for computing the sum of an arithmetic progression of n terms with first term a and common difference d?

What is the algorithm for computing the sum of an arithmetic progression of n terms with first term a and common difference d? -------------- Step 1 Set S = a, k = 1, and t = a. Step 2 while k < n (a) Replace t with t + d (b) Replace S with S + 1 (b) Replace k with k + 1 ...continues

Combinations : Tacos

In San Diego, tacos consist of meat topped by any or none of cheese, sauce, beans, and lettuce. In how many ways can tacos be ordered? Why?