Discrete Mathematics Answers

Consider the following relations on {1, 2, 3, 4}.

R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)}

R2 = {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}

R3 = {2,4),(4,2)}

R4 = {(1,2),(2,3),(3,4)}

R5 = {(1,1),(2,2),(3,3),(4,4)}

a)  Which of these relations are reflexive? Justify your answers.

b)  Which of these relations are symmetric? Justify your answers.

c)  Which of these relations are antisymmetric? Justify your answer.

d)  Which of these relations are transitive? Justify your answers.

A. Provide formal of the validly of each of the following arguments.

1. I shall either play basketball or i shall go to the mall and watch the movie. therefore i shall either play basketball or go to a mall.
2. the Chocolate hills are not chocolate if I'm not the president of the Philippines. I'm not the president of the Philippines. therefore the Chocolate hills are chocolates.
3. if the summer is hot when we won't go on vocation in may. we'll either go on vacation inmay or we'll buy a boat (perhaps both). therefore, if the summer is hot, we'll buy a boat.
4. if Anna encore or write a program, she get an a. she's encoding and reading her lessons. therefore she'll get an A.

What is the solution for the recurrence relation a_n=2a_{n−1}−1

an

​=2an−1

​−1 with a_1=3

a1

​=3 .

C. Let p and q be proposition

p: 4 is a rational number

q: √3 is an irrational number

Express each of these proposition as an English sentences:

1. ~p
2. p∨ q
3. p ∧ q
4. p → q
5. p ↔ q

Show that the square of an even number is an even number using direct proof

An=2*n+an-1,A1=1

1.     Let p and q be propositions. p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives.

a.      You do not drive over 65 miles per hour.

b.     You will get a speeding ticket if you drive over 65 miles per hour.

c.      If you do not drive over 65 miles per hour, then you will not get a speeding ticket.