Draw the Hasse diagram representing the partial ordering {(a, b) | a divides b} on {1, 2, 3, 4, 6, 8, 12}.

Discrete Mathematics Basics
1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where ${\displaystyle (a,b)\in R}$ if and only if
I) everyone who has visited Web page a has also visited Web page b.
II) there are no common links found on both Web page a and Web page b.
III) there is at least one common link on Web page a and Web page b.

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.
a) the set of sophomores taking discrete mathematics in your school
b) the set of sophomores at your school who are not taking discrete mathematics
c) the set of students at your school who either are sophomores or are taking discrete mathematics
Use these symbols: ${\displaystyle \cap \cup }$

Let A, B, and C be sets. Show that ${\displaystyle (A-B)-C=(A-C)-(B-C)}$

How many elements are in the set { 0, { { 0 } }?

Let R be the relation from X={1,2,3,5} to Y={0,3,4,9} defined by xRy if and only if ${\displaystyle x^2=y}$

Let ${\displaystyle n\ge 8}$. Give a ${\displaystyle big-\Theta }$ estimate for the number of circuits of length 8 in Kn. ${\displaystyle \Theta \left(n\right)\Theta \left(n8\right)\Theta \left(8\right)\Theta \left(8n\right)\Theta \left(8n\right)}$

Express the following in set-builder notation:
a) The set A of natural numbers divisible by 3.
b) The set B of pairs (a,b) of real numbers such that ${\displaystyle a+b}$ is an integer.
c) The open interval ${\displaystyle C=(-2,2)}$.
d) The set D of 20 element subsets of N.