Discrete Mathematics Answers

a_n-3a_n-1-4a_n-2=4.3n

Use breadth-first search to produce a spanning tree for

each of the simple graphs in Exercises 1 3-15. Choose

a as the root of each spanning tree. 

Let g be a function from Z+ (the set of positive integers) to Q (the set of rational numbers) defined by (x, y) element of g iff y = (g is a subset of Z+ mapped with Q) and let f be a function on Z + defined by (x, y) element of f iff y = 5x2 + 2x – 3 (f subset of Z+ mapped with Z+)

Which one of the following statements regarding the function g is TRUE? 

(Remember, g is a subset of Z+ mapped with Q.)

1. g can be presented as a straight line graph.

2. g is injective.

3. g is surjective.

4. g is bijective.

(a) In how many ways can a committee of 3 faculty members and two students be selected from 7 faculty members and 8 students

(b) How many ways are there to distribute 12 different books among 15 people if no person is to receive more than one book 

 Design a single error correcting code for m=3 & n=7

Show that ¬ (P"\\iff"Q)"\\iff"(P V Q) Λ ¬(P Λ Q) "\\iff"(P Λ ¬Q) V (¬ P Λ Q) without using truth table

Find the generating function of recurrence relation an+1_an=3n ,n less than 0 where ao=1

Basic Counting Principle

6.     How many different car license plates can be constructed if the licenses contain three letters followed by two digits if:

a.) Repetitions are allowed;

b.) repetitions are not allowed.

7.     Two dice are rolled, one blue and one red. How many outcomes have either the blue die 3 or an even sum or both?

8.     How many integers from 1 to 10,000, inclusive, are multiples of 5 or 7 or both?

9.     Prove that if five cards are chosen from an ordinary 52-card deck, at least two cards are of the same suit.

10. Eighteen persons have first names Adrian, Jheo and Ghimel and last names Ablir and Testor. Show that at least three persons have the same first and last names.

1.     Three departmental committees have 6, 12, and 9 members with no overlapping membership. In how many ways can these committees send one member to meet with the president?

2.     Two dice are rolled, one blue and one red. How many outcomes give the sum of 5 or the sum of 9?

3.     The options available on a particular model of a car are five interior colors, six exterior colors, two types of seats, three types of engines, and three types of radios. How many different possibilities are available to the consumer?

4.     Two dice are rolled, one blue and one red. How many outcomes are possible?

5.     How many times is How many eight-bit strings read the same from either end? (An example of such an eight-bit string is 01111110. Such strings are called palindromes.)