Discrete Mathematics Answers

List the members of the set

I is the set of integers that lies between -1 and 5

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.

1. {0}

2. {0, { a } , { 0, a }}

3. {0, { a } }

4. {0, { a }, { b }, { a, b }}

In a party, there are 12 people with white shirts and 7 people with red shirts;

4 people have black shoes and white shirts;

5 people have black shoes and red shirts;

the total number of people with white or red shirts or black shoes is 21.

How many people have black shoes?

In a party, there are 12 people with white shirts and 7 people with red shirts;

4 people have black shoes and white shirts;

5 people have black shoes and red shirts;

the total number of people with white or red shirts or black shoes is 21.

How many people have black shoes?

Prove that the premises P → Q, Q → R, S → ¬R and P ∧ S are inconsistent.

1.)Determine if the proposition is satisfiable or not by providing any possible combination of inputs that yields a TRUE result.

(p ∧ q) ∨ (¬p ∧¬q)→r

2.)Prove or disapprove the given proposition using a truth table or rules of logic.

¬(¬p ∧ q) ∨ q ⇔ q → p

7. Express these system specifications using the proposi tions p "The message is scanned for viruses" and "The message was sent from an unknown system together with logical connectives (including negations).

a) "The message is scanned for viruses whenever the message was sent from an unknown system." b) "The message was sent from an unknown system but

it was not scanned for viruses. c) "It is necessary to scan the message for viruses when ever it was sent from an unknown system.

d) "When a message is not sent from an unknown system

it is not scanned for viruses.

7. Express these system specifications using the proposi tions p "The message is scanned for viruses" and "The message was sent from an unknown system together with logical connectives (including negations).

a) "The message is scanned for viruses whenever the message was sent from an unknown system." b) "The message was sent from an unknown system but

it was not scanned for viruses. c) "It is necessary to scan the message for viruses when ever it was sent from an unknown system.

d) "When a message is not sent from an unknown system

it is not scanned for viruses.

11•j=1(mod 4). Find j

Which of the following best describes inductive reasoning?

a. Using logic to draw conclusions based on accepted statements

b. Accepting the meaning of a term without definition

c. Defining mathematical terms to correspond with physical objects

d. Inferring a general truth by examining a number of specific examples