Discrete Mathematics Answers

Define
(a) Graph; (b) Null graph; (c) Isolated vertex; (d) Pendant vertex;
(e) Pseudo-graph; (f) Directed graph; (g) Adjacent nodes; (h) Incident edges;

Draw a Venn diagram of sets B,A and C where A . ⊆ ,B A ∩ C ≠ φ, B∩ C = φ
What is the universal set you have chosen? Justify your choice of sets in the
diagram.

(p->(q^r))^(not p->not q^not r))

Let A = {1; 2; 3; 4; 5; 6; 7; 8; 9; 10} and B = {1; 2; 3; 4}. Let R be the relation on P (A)
defined by:
For any X,Y element in P(A), XRY if and only if X-B = Y-B.
How many equivalence classes are there? Explain

GreenRecycle.com is a recycle firm whose main business is recycling paper. There is a particular standard to grade the recycled papers in the firm, which grades the papers as P11, P12, P13, P21, P22, P31 and P32.

a) Model the set of the papers
b) Three warehouses are used to store the papers and special accounts are assigned to the warehouses as given by:
warehouse = { X, Y, Z }
Account_warehouse = { (123,X), (456,Y), (789,Z) }

If the papers being stored in the warehouse are given as:
paper_warehouseAccount = { (P11,123), (P12,123), (P13,456), (P21,789), (P22,789), (P31,789), (P32,123) }

Find the papers stored in warehouse A.

(A \ B )∪ C = A \ (B∩ C )for any three sets A,B and C
Is the statement true or false?
Give justification in support of your answer.

a. Minimize the following problems using the Karnaugh maps method.
Z = f (A, B, C) = + B + AB + AC

a) Simplify the Boolean function F = AB + (AC)′ + AB ′C(AB + C).

For any two sets A and B , in a universal set U , prove that
A ⊆ B ⇔ A ∪ B = B.

Q : 1) Construct the call graph for a set of seven telephone
numbers 555-0011, 555-1221, 555-1333, 555-8888,
555-2222, 555-0091, and 555-1200 if there were three
calls from 555-0011 to 555-8888 and two calls from
555-8888 to 555-0011, two calls from 555-2222 to
555-0091, two calls from 555-1221 to each of the
other numbers, and one call from 555-1333 to each of
555-0011, 555-1221, and 555-1200.

Q : 2) Find the sum of the degrees of the vertices of each graph
in Exercises 1–3 and verify that it equals twice the number
of edges in the graph.

Q : 3) Draw these graphs.
a) K7 b) K1,8 c) K4,4
d) C7 e) W7 f) Q4