Discrete Mathematics Answers

1.4 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10) A = {90, 92, 94, 96, 98, 100}, B= {91, 93, 95, 97, 99}, C = {90, 94, 98}

1.4.1 What is (A ∩ C)c

1.4.2 What is (B ∪ C)c

Find the inverse of the encrypting function

F(x) =(5-x) mod 26 , 0<=x<=25

And use it to decrypt the massage '' ZRQUBFNB''

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