Discrete Mathematics Answers

1. Express the following statements using quantifiers.

A. All cats have fleas.

B. No one in this class knows how to speak Mandarin.

2.Form the negation of each statement without applying negation to the left of any quantifier.

3. Express each negation in simple English.

Part 2

1. Given A = {4, 8, 12, 16} and B = {6, 12, 18, 24}, determine the following:

a. A U B

b. A ∩ B

c. A - B

d. B - A

Use resolution to show the hypotheses “Allen is a bad

boy or Hillary is a good girl” and “Allen is a good boy or

David is happy” imply the conclusion “Hillary is a good

girl or David is happy.”

Let A = {a, b, c}, B = {x, y}. Find the following:

1. A × B

2. B × A

Use the rule of inference to obtain conclusion from the each of the set of premises

“If I play hockey, then I am sore the next day.”

“I use the whirlpool if I am sore.”

“I did not use the whirlpool.”

How many 3-digit numbers can be formed from digits 1 – 5 if:

a. If repetition is allowed?

b. If repetition is not allowed?

How many possible passwords are there for the following conditions: 3

digits followed by 2 letters followed by 4 digits? (3 pts)

false statement by finding a counterexample

1. x/x=1
2. x+3)/3=x+1
3. √(x^2+16)=x+4

1. a) Determine whether the following proposition is logically equivalent or not using the truth table.

((p⟶q)v(q⟶p))⇔p⟷q

b) Construct a truth table to determine whether the following compound statement is a tautology, a contradiction or a contingency.

~(p∧r)⟶~(q∨r)

c) Use the laws of logic to establish the following logical expression.

~(p∨q) v (~p∧q)⟺~p

Determine whether the statement is logically equivalent using truth tables. [ (~P ∧ Q ) ⊕ P ] AND ( ~P V∧ Q)

Use Euclidean algorithm to determine the gcd (4076, 1024)