Discrete Mathematics Answers

Identify if the following statements are predicate logic. Give a domain of discourse for each propositional function.

(x+2)^2 is a prime number?

What is the 10-bit string for the complement of 10-bit string 1010101010.

Let 𝑓(𝑥) = 2𝑥²−3𝑥+7 / 5x²-2x. Find 𝑓(3).

Let g(x) = 5 / x-4. find the domain of g(x)

Show that the propositions p1,p2,p3,p4, and p5 can be shown to be equivalent by proving that the conditional statements p1→p4, p3→p1, p4→p2, p2→p5, and p5→p3 are true.

Let P be the property “is a prime number” and O be the property “is an odd integer.” Consider the sets A = {x ∈ N : P(x)} and B = {x ∈ N : O(x)}. 1. Examine A and B with respect to the subset relation. What can you conclude? Justify your answer. 2. Are A and B equal? Justify your answer.

2. A random variable X can have values -4. - 1, 2, 3 and 4, each with probability 1/5 Find: the density function f_{Y} . the distribution function F_{y} , the mean E(Y) . and the variance sigma_{y} ^ 2 , of the random Y = 3X ^ 3

a_n=3a_n-1+(n²+n-2)3ⁿ

List the members of the following sets.

1. {x| x is real numbers and x²=1}

2. {x| x is an integer and -4 < x ≤ 3}

Let Q(x, y) denote the statement “x is the capital of y.”

What are these truth values?

a) Q(Denver, Colorado)

b) Q(Detroit, Michigan)

c) Q(Massachusetts, Boston)

d) Q(New York, New York)