Q11-A-8 points Does the following graph have an Euler Circuit? If not, add extra edges to make it an Eulerian Graph. Explain. Set of Vertices V={A,B,C,D,E,F,G} Set of Edges E={ AB, AD, BE, BG, BC, BD, DB, CG, CE, CD, EF, EG, FG}.  

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

Suppose you are working with a logic family that has the following specifications: VDD 1.8 V VIH 1.17 V VIL 0.63 V VOH 1.2 V VOL 0.45 V Suppose the voltage of a signal is 0.5 V.  Select the two statements that are correct (one for the driver and one for the receiver)

Q12-B-7 points Find the coefficient of when the following expression is expanded using the Binomial theorem:

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 = 1 ns? Assume the delay from inputs changing to output changing is negligible.

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?

Q3-C 8 points Let ​A​ = {0, 1, 2, 3, 4} and let ​R​ be the relation with digraph with vertex set V and edge set E. Set of Vertices V = {0, 1, 2, 3, 4} Set of Edges E = {(0,0), (1,1), (2,2), (0,4), (4,0), (0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (0,3), (3,0), (1,3), (3,1), (0,2), (2,0)} Note: (2,2) means a loop from the vertex 2 to itself, (2,3) means an edge from vertex 2 to vertex 3, etc, . . .  Test this relation for the following properties: reflexive symmetric transitive

Given the following circuit: If the inputs are E=0, A=0 and B=0, what is the value of Y?

Q6-A-8 points  In a certain state, all license plates consist of from 4 to 6 symbols chosen from the 26 letters together with the ten digits (0-9) a) How many license plates are possible, repetition allowed? b) How many license plates have at least one repeated symbol?  

Q1-B-7 points Determine whether the relation D is reflexive, symmetric, transitive, or none and justify your answer: Let D represent the ‘divides’ relation on the set of positive integers   . For all m, n