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Suppose that R and S are two relations on the set A = {a, b, c, d}, where R = {(a,b),(a,d),(b,c),(c,c),(d,a)}, and S = {(a,c),(b,d),(d,a)}.
A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review.
Find the exponential generating function for Sn,r the number of ways to distribute r distinct objects into n distinct boxes with no empty box.
Definition: For any E in X, where X is any set, define M(E) = infinity if E is an infinite set, and let M(E) be then number of points in E if E is finite.
Show that if A is equivalent to B and C is equivalent to D, then A x C is equivalent to B x D.
If there are 10 students who own both a cellphone and a digital tv, but not a laptop, and there are 20 students who don't own a cellphone.
A computer lab contains the following computers – a Hewlett Packard, a Compaq, a Sony, a Dell and 3 different models of Macs.
Show that if 7 integers are selected from the first 10 positive integers there must be at least 2 pairs of these integers with the sum 11.
Find the condition for the modulus n, for which the congruence 2x+6 = 4 (mod 8) actually does have the solution set {x; x = -1 (mod 8)}.
Write the given permutation as the product of disjoint cycles. Provide complete and step by step solution for the question.
Let Y=(u v/u^4=v^3=1,uv=u^2v^2) show that u=1, deduce that v=1 and conclude that Y=1
Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for all a in A.
Use the breadth-first search algorithm to find a spanning tree for the following connected graph. Start with A and use alphabetical order.
Without writing them down what are the number of subsets of the set A = {a, b, c, d, e, f}? Of set B = {a, b, c, d, e, f, g, h, i, j}?
A sinking fund is established to obtain $75,000 in five years. The interest rate is 10% and payments are made quarterly.
The parentheses in R(x) is used to distinguish the ring R(x) of rational functions from the ring R[x] of polynomials.
Assuming that the nine friends consist of five single people and 2 married couples. If she invites a husband or wife she must invite the spouse.
If alpha is an r-cycle, show that alpha^r = (1). [There's a hint that If alpha = (i sub 0 ... i sub r-1), show that alpha ^k(i sub 0) = i sub k.]
A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different meals consisting of one salad, one main dish.
In how many ways can a six-letter security password be formed from letters of the alphabet if no letter is repeated?
Let S be a set of people. For x, y E S, define xRy to mean that x = y or x is a decendant of y. Prove that R is a partial order on S.
A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation,no engines, one engine, two engines.
In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components.
To prevent false alarms, the system is designed so that three or more of the sensors must sense over temperature before a warning signal is given.
How many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?