Discrete Mathematics Answers

Determine if the following argument is valid using truth tables

p ←→ q
p∧ ∼ q
_________
∴ r

Determine if the following argument is valid using truth tables.


p −→ r
r
_______
∴ p

Determine if the following argument is valid using truth tables.

p ∧ q → r
__________
∴ q → r

Let D = {1, 2, 3}. The domain of the variables x and y will be D. Is it possible to find a predicate P(x, y) such that ∃y ∀x P(x, y) is true but ∀x ∃y P(x, y) is false? Explain

Let D = {1, 2, 3}. The domain of the variables x and y will be D.

Give an example of a predicate P(x, y) such that ∀x ∃y P(x, y) is true, but ∃y ∀x P(x, y) is false

How many 8-bits sequences that start with the same two bits or their fourth and fifth bits are equal or end with the same two bits are there?

If we reduce the number of elements by two, the number of permutations reduces thirty times. Find the number of elements.

In a lottery, players win a large prize when they pick four digits that match, in the correct order, four digits selected by a random mechanical process. A smaller prize is won if only three digits are matched. What is the probability that a player wins the large prize? What is the probability that a player wins the small prize?

determine that wheter the functions from real numbers to real numbers are one to one
f(n)=n^3
f(n)=n^2+1

Determine if the statements are valid arguments.

I just got my ticket to the concert but if the number of tickets sold is more than 75% of its capacity, I will not want to go because it will be too crowded and I don’t like it. If my friend Alex goes then I will go too. I can’t believe this but yesterday I heard that Alex got tickets too and is going. The concert is sold out as of this morning. After so much reflection, I will go to the concert.