Assume that X can be polynomially reduced  to Z, in that there exists a function f such that     forall  x,   x in X   iff   f(x) in Zand f can be computed in time polynomial in the size of x. Which inferences are then valid?

Consider how we could decide the 3COL problem:  generate one color map, and check if it is a valid coloring;  if not, then reuse the space to generate a second color map,  and check if it is a valid coloring; if not,  then reuse the space to generate a third color map, etc, etc,  until either some color map has been found valid,  or all color maps have been found invalid. Observe that a color map can be generated and checked in polynomial time. What can we then say about each of the below claims (where PSPACE are the problems that can be decided in polynomial space)?   

Finally, some questions about a probabilistic problem. Given a sequence of coin flips, we define a doubleton as two consecutive Hs with no H immediately before or after, or two consecutive Ts with no T immediately before or after. For example, the sequence TTHTTTHHHHTTHTHHThas 3 doubletons (boldfaced). Assume that we toss a fair coin n times (n  >= 3). With X a random variable denoting the number of doubletons in the resulting sequence, we want to calculate E.  For that purpose, for each i in 1..n we define an indicator random variable X_i for the event that toss i starts a doubleton; thus E = 0 andX = \sum_{i=1}^n X_i.(Observe that when n = 3 we have E =  4/8 = 1/2 since each of the sequences HHT and TTH and HTT and THH has 1 doubleton, while each of the sequences HHH and TTT and HTH and THT has 0 doubletons.)

Exam 4- Chapters 14, 15, &16

Exam 1- Chapters 6, 17 & 18

Henry’s duties include mixing a variety of chemicals for the products and treatment ointments and mixtures they use on clients. When mixing these chemicals, Henry should avoid all EXCEPT which of the following?

            Linda’s manager told her to use caution when unpacking supplies on Tuesday mornings. “Make sure to pay attention to certain products and chemicals that are incompatible,” he said. What should Linda make sure she does with these types of products?

Which of the following is NOT a trait associated with liturgical protestant religions?

Which of the following is true in the Islamic faith?

A symbolic cloth covering placed on the casket representing both the righteousness of Christ bestowed at one’s baptism and the equality of all men before God is a