e$)-x_2+x_{4}1$

$x1,x2$ and $x3$ are binary variables. Which statement is true about this constraint $x1x2+x3?$

a$)$ When $x2$ and $x3$ are selected, $x1$ must be selected

b$)$ When $x1$ is selected, both $x2$ and $x3$ must be selected

c$)$ When X$1$ is selected, either X$2$ or X$3$ must be selected

d$)$ If $x2$ is selected, then $x3$ must be selected as well

e$)$ When $x2$ and $x3$ are selected, $x1$ can not be selected

$x1,x2$ and $x3$ are binary variables. Which statement is true about this constraint $2x1x2+x3?$

a$)$ When $x2$ and $x3$ are selected, $x1$ must be selected

b$)$ When $x1$ is selected, both $x2$ and $x3$ can not be selected

c$)$ When $x1$ is selected, $x2$ does not have to be selected

d$)$ If $x2$ is selected, then $x3$ must be selected as well

e$)$ When $x2$ and $x3$ are selected, $x1$ can be selected

Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices $S$ and $T.$ Which one will be reported by Dijkstra's shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex $v$ is updated only when a strictly shorter path to $v$ is discovered.

$11$

a$)$ SDT

b$)$ SBDT

c$)$ SACDT

d$)$ SACET

e$)$ SBFT

When using Dijkstra's algorithm to find shortes path in a Graph, which of the following is NOT true?

a$)$ It can find shortes path within the same graph data structure

b$)$ Every time a new node is visited, we choose the node with smallest known distance $/$ cost $($weight$)$ to visit first.

c$)$ Shortest path always passes through least number of vertices

d$)$ The graph needs to have a non$-$negative weight on every edge.

e$)$ Shortest path to a visited node might be updated based on updated information $/$ new iteration of the agorithm.

Consider the below non$-$directed graph. There are multiple paths from any node to any other node. Based on the shortest path algorithm, Dijkstra's algorithm, what is the short path from $"a"$ to $"g"?$

a$)$ a$-$c$-$e$-$g

b$)$ a$-$d$-$f$-$g

c$)$ a$-$c$-$f$-$g

d$)$ a$-$d$-$c$-$f$-$g

e$)a-c-g$