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

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)  

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)  

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.

Given: A basic 3:8 decoder has address inputs A2:0 and outputs Y0, Y1, …, Y7. Suppose A2 = 0, A1 = 0 and A0 = 1.  Select the correct answer.

True of False: A combinational circuit has memory.

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?

Convert 4210 to an 8-bit two’s complement number (ex: “01101110”)

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?