Discrete Math - Please do the followings

0.1 A procedure for connecting up a {possibly disconnected]I simple graph and creating a spanning tree can be modeled as a state machine whose states are nite simple graphs. A state is nal when no further transitions are possible. The transitions are determined by the following rules: 1. If there is an edge {u, v} on a cycle, then delete {u, U}. 2. If vertices u and v are not connected. then add the edge {u, D}. For any graph 0", let 9 be the number of edges in G'. c be the number of connected components it has. and s be the number of cycles. Select all of the following quantities that are strictly decreasing at each transition of the state machine. [3+9 3c+2e (+5 0.2 Suppose that a set B is dened as B ::= B 1 x 32 X 33. Choose all of the following that is true. IN = I31 '32 ' 33' |B|=|31| 'le| '|33| |B|=|leBsz3| 0.3 f: A -> Bisabijection 4:) |A| = |B|. True or False? Q4 How many ways are there to pick one number out of 6 choices, choose 2 colors from 7 color options, and permute a sequence of 5 numbers