Q4-B-7 points We are given an urn with three balls: two blue balls labeled B1B_1​ and B2B_2​, and one white ball labeled WW. A ball is drawn, replaced, and then another ball is drawn and its color recorded. Let B1WB_1W represent the outcome where the first ball drawn is B1B_1​ and the second ball drawn is WW. Since the ball is returned to the urn before the second is draw, each outcome is equally likely. List all nine possible outcomes of this experiment.     

Q1-A-7 points Determine whether the relation , is reflexive, symmetric, transitive, or none and justify your answer: Let denote the congruence modulo 4 relation on the set of integers For all integers

Q9-C-8 points Prove the following Identity:

Q7-B-8 points A group of 12 students is available. A team of 4 students is to be selected and then arranged in a line for a photo. In how many ways can this be done?

Suppose the capacitance in a digital circuit is doubled (the capacitance is now twice what it was before).  If nothing else changed, how does that affect the power consumption?

True of False: A combinational circuit has memory.

A timing diagram is given for inputs to a basic D Flip-Flop. What is the value of the Q output of the D Flip-Flop at time = 9 ns? Assume the delay from inputs changing to output changing is negligible.

Q8-C-8 points a) How many integers from 1 to 1000 are multiples of 2 or 9? b) How many integers from 1 to 1000 are neither multiples of 2 nor multiples of 9?                  

Q13-A-8 points Use Kruskal’s algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) The following matrix represents the weighted graph of this question:

True of False: A sequential circuit does not have state.