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}.      

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?

Given: A 16:1 multiplexer has data inputs D0, D1, …, D15, select inputs S3:0, and output Y.  It is implemented using tristate buffers. What is used to enable the tristate buffer that is connected to D5?

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

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

Q2-C-7 points Consider the “Divides” Relation on the following set A. A = {1, 2, 4, 5, 10, 15, 20} Draw the Hasse Diagram. (You can list the set of vertices, and edges for this diagram)  

Given: An 8:1 multiplexer has data inputs D0, D1, …, D7, select inputs S2:0, and output Y. Suppose D0 = 1, D1 = 0, D2 = 0, D3 = 0, D4 = 1, D5 = 0, D6 = 1, D7 = 1, S2 = 0, S1 = 1, and S0 = 1.  What is the value of Y?

Given: An 8:1 multiplexer has data inputs D0, D1, …, D7, select inputs S2:0, and output Y. Suppose D0 = 1, D1 = 0, D2 = 0, D3 = 0, D4 = 1, D5 = 0, D6 = 1, D7 = 1, S2 = 1, S1 = 1, and S0 = 0.  What is the value of Y?

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 = 13 ns? Assume the delay from inputs changing to output changing is negligible.