Discrete Mathematics Answers

If A = {1, 2, 3, 4, 6, 12} then define a relation R by aRb if and only if a divides b. Prove that R is a partial order on A.

Suppose that A = {2, 4, 6}, B ={2, 6}, C ={4, 6}, and D ={4, 6, 8}. Determine which of these sets

are subsets of which other of these sets.

A pet store keeps track of the purchases of customers over a fours hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or product for a different kind of pet. He found!

83 purchased a dog product

101 purchased a cat product

22 purchased a fish product

31 purchased a dog and a cat product

8 purchased a dog and a fish product

10 purchased a cat and a fish product

6 purchased a dog, a cat, and a fish product

34 purchased a product for a pet other than a dog, cat, or fish.

Draw a Venn diagram to find that:

(1) How many purchases were for a dog product only?

(ii) How many purchases were for a cat product only?

How many purchases were for a dog or a fish product?

(iv) How many purchases were there in total?

Determine how many bit strings of length 5 can be formed, where the first bit is 0 and three consecutive 0s are not allowed.

For the relation R = {(p,p) ,(q,p),(q,q),(r,r),(r,s),(s,s) ,(s,m) ,(m,m)}

1.Using warshall algorithm find the transitive closure R* of R

2.write matrix representation of R*

3.Check whether the relation of R* is an equivalence relation or a partial order.

range of the function f(x) = 5x − 3 defined by the domain {0,1,2}

For each of the following sets,

a) S={1,2,3}, T ={a, b, c}

b) S={a, b}, T ={1,2,3,4}

c) S={1,2,3,4}, T ={a, b}

Determine whether

1. There is a one-to-one function f:S→T;

2. There is an onto function f:S→T; and

3. If there is a bijective function f:S→T.

4. For each (1–3) if such a function exists, explicitly give it. If no function exists give a short explanation?

. What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached? a) if x + 2 = 3 then x := x + 1

. What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached? a) if x + 2 = 3 then x := x + 1

1. Find these terms of the sequence {an}, where an =

2 · (−3)n + 5n.

a) a0

b) a1

c) a4

d) a5