Discrete Mathematics Answers

Let R be the partial order relation defined on A = {2, 3, 4, 5, 6, 8, 10, 40}, where xRy means x | y.
i.Draw the Hasse diagram for R.
ii.Find the upper and lower bounds of {4, 8}.

Find the smallest equivalence relation on {1, 2, 3} that contains (1, 2) and (2, 3).

Let G be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent if |i-j|=8 or |i-j|=12. The number of connected components in G is
a)8
b)12
c)25
d)4

How many solutions are there to the equation
x1+x2+x3+x4+x5=21,
where xi, i=1,2,3,4,5, is a nonnegative integer such that
a)x1>=1?
b)xi>=2, for i=1,2,3,4,5?
c)0<=x1<=10?
d)0<=x1<=3, 1<=x2<4, and x3>=15?

In how many ways can a set of two positive integers less than 100 be chosen?

How many different strings can be made from the letters in ORONO, using some or all of the letters?

Say a slope of a line is three over one. I know you can (on a graph) go up three, over one; up three, over one; up three, over one. I also understand you can go negative three, negative one; negative three, negative one; negative three, over one. Can you go both ways or only one direction? Thank's!

Find the solution to the recurrence relation a_n=〖-3a〗_(n-1) 〖-3a〗_(n-2) 〖-a〗_(n-3) with initial conditions a_0=1,a_1=-2 and a_2=-1

A binary relation on a set that is reflexive and symmetric is called a compatible relation. Let A be a set. A cover of A is a set of non-empty subsets of A, say { A_(1,) A_2,A_3……A_n} such that union of A_i's is equal to A. Suggest a way to define a compatible relation on A from a cover of A.