For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R:

----------------------------------------

Row 1: 1 0 1

Row 2: 1 1 0

Row 3: 0 1 1

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Which of the properties (reflexive, antisymmetric, t READ MORE »

Let G be a graph. Then G = (V, E), where V and E are the vertex set and edge set, respectively, of G.

The complement of G, which we will refer to as "G bar," is the graph (V, E bar), where V is the vertex set of G bar (i.e., the vertex set of G bar is identical to the vertex set of G) and E bar i READ MORE »

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R:

----------------------------------------

Row 1: 1 0 1

Row 2: 1 1 0

Row 3: 0 1 1

-----------------------------------------

Determine whether R is a partial order. If it is, dra READ MORE »

Do the following:

(1) Evaluate Int(P(x, y) dx + Q(x, y) dy) over the curve C, where P(x, y) = y^2, Q(x, y) = 3x, and C is the portion of the graph of the function y = 3x^2 from (-1, 3) to (2, 12). Here, "Int" stands for integral.

(2) Use the Divergence Theorem to evaluate the surface integral READ MORE »

Let B = {[(-1^n](n)/(n + 1): n = 1, 2, 3, ...}.

(a) Find the limit points of B.

(b) Is B a closed set?

(c) Is B an open set?

(d) Does B contain any isolated points?

(d) Find the closure of B.