Discrete Mathematics Answers

Let A = {2, 4} and B = {6, 8, 10} and define relations R and S from A to B as follows: for all (x,y) EA x B. XRyoxly for all (x,y) EA x B x Syy-4 = x State explicitly which ordered pairs are in A x B. R, S, RUS and Ros. And draw the Coordinate Graph, Arrow Diagram & Directed Graph for each.

A.   Use quantifiers to express the following statements.

1.    Every student enrolls in a math class.

2.    There is a student in a class who drops a math course.

3.    Every student in this class wears an ID.

4.    At least one student in this class requests for uniform pass.

5.    Every student access the free wifi connection in the campus.

Can a simple graph exist with 15 vertices each of degree five?

Draw these graphs.

a) K7 b) K1,8 c) K4,4

d) C7 e) W7 f ) Q4

Let P(x) be the statement “x = x²." If the domain con- sists of the integers, what are these truth values? c) P(2) f) VxP(x) a) P(0) b) P(1) d) P(-1) e) 3x P(x)

I. Use quantifiers to express the following statements.

1. Every student enrolls in a math class.

2. There is a student in a class who drops a math course.

3. Every student in this class wears an ID.

4. At least one student in this class requests for uniform pass.

5. Every student access the free wifi connection in the campus.

Let A = {0, 2, 4, 6, 8}, B = {0, 1, 2, 3, 4}, and C = {0, 3, 6, 9}. What are A ∪ B ∪ C and A ∩ B ∩ C?

Draw a Venn diagram that represents V, the set of vowels in the English alphabet, where set of vowel is {a,e,i,o,u}

(i). In MA161 class, the lecturer gave the following proposition. Let A (x, y) be “ y is greater than or equal to x ”. The domain for the proposition is the set of nonnegative integers. The students were tasked to determine what are the truth values of ∃y ∀xA (x,y) and ∀x∃yA(x,y ) ?