Q9-C-8 points Prove the following Identity:

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

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

How many D flip-flops are needed to represent 30 different states?

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:

Q11-B-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} Set of Edges E={ AB, AE, AD, AC, BC, BD, BE, CD}.      

Q11-B-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} Set of Edges E={ AB, AE, AD, AC, BC, BD, BE, CD}.      

Q3- A 8 points Let ​A​ = {2, 5, 8} and let ​R​ be the relation with digraph with vertex set V and edge set E. Set of Vertices V = {2, 5, 8} Set of Edges E = {(2,2), (5,5), (8,8), (2,5), (2,8), (5,8)}. Note: (2,2) means a loop from the vertex 2 to itself, (2,8) means an edge from vertex 2 to 8, etc, . . .  Test this relation for the following properties: reflexive symmetric transitive

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.

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?