Discrete Mathematics Answers

Suppose that the statement p → ¬q is false. Find all combinations of truth values of r and s for which

(¬q → r) ∧ (¬p ∨ s) is true.

Let p, q, and r be true, false and false, respectively. Determine the truth value of the

following?

a.) (p → q) ∧∼ r

b.) q ↔ (p ∧ r)

Write each of the propositions in the form “p if and only if q”:

a.) For you to get a passing mark in this course, it is necessary and sufficient that you

learn how to solve mathematics problems.

b.) If you read the newspaper every day, you will be informed, and conversely.

Translate these statements into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consists of the students in your class.

A student in your class does not want to be rich.

[LET R(x): X WANTS TO BE RICH]

Draw the Hasse diagram foe 2,3,4,5,10,12,25,30?

Find the Cartesian product A × B × C where A = (0, 1), B = (1, 2) and C= (0, 1, 2)

Solve the recurrence relation of an=3an-3an-2-an-3 n>=3 a0=1 a1=-2 a2=-1

Let 𝑈 = {𝑎, 𝑒, 𝑖, 𝑜, 𝑢, 3, 6, 9, 12}, 𝐴 = {𝑜, 𝑢, 3, 12}, 𝐵 = {𝑢, 9, 6, 𝑎}, 𝑎𝑛𝑑 𝐶 = {𝑢, 12, 𝑖, 𝑜}.

1. Find 𝐶 ∪ 𝐴

2. Find (𝐶′ ∩ 𝐵) ∪ 𝐶

3. Find {(𝐵′ ∪ 𝐴)′ − 𝐴 ∪ (𝐵 ∩ 𝐵′)}

Make a truth table to determine the logical equivalence of the statements.

1. ~ P → Q ↔ P ∨ Q
2. ~ (P → Q) ↔ P ∨ ~Q.

Prove that a real number 𝑥 is irrational if and only if 5𝑥 is irrational