Discrete Mathematics Answers

.List all subsets of{ , , , , },containing but not containing

List all subsets of{0,1,3}.How many do you get?

Use set builder notation to give a description of this set A = {0, 3, 6, 9, 12}

Express this gaming system requirement using predicates, quatifiers and logical connectives: "When there are less than 2 gigabytes of available RAM, an error message is displayed"

{x | x is a real number such that x4 = 1}

Find the truth value of the statements using the given domain of discourse.

1.Suppose P(x) is the predicate x + 2 =2x and the domain is a set of {1,2,3}.

2.If P(x) is the predicate x²-3x-4=0 and the domain is a set of {1,2,3,4}.

Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.

2a) {(a, b) ∣ a and b are the same age}

2b) {(a, b) ∣ a and b speak a common language}

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

1. The movie won the Academy Award for the past 2 years.
2. 1 + 3 = 4
3. (x+2)² is a prime number.
4. man is mortal
5. not all people are dishonest.

II.) Convert the given argument into four type of nested quantifier.

"Every Math Teacher is like by some students"

(note: you may take different types of approach in your sentences but the thought of the quantifiers must still be there)

Let the set U = {1, 2, 3, 4, 5}, be the universe. Let Y = {(n+2)| n = 2, 3} 5 and X = {3, 4}. Write the following sets using set builder notation

1.      What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?

a)      if x + 2 = 3 then x := x + 1