If G is a DAG we denote by τ (G) the number of distinct topological sorts of G. Now let G = (V, E) be any DAG. An add-one-vertex operation on G constructs a digraph G 0 = (V 0 , E 0 ) such that • G 0 is also a DAG. • We add exactly one new vertex, call it z that is, V 0 = V ∪ {z}, z ∈ / V . • We add some (possibly 0) new directed edges, that is, E 0 ⊇ E. (a) Prove that for any DAG G = (V, E) there is a way to perform an add-one-vertex operation on G such that the resulting DAG G 0 has the same number of topological sorts, i. e. τ (G 0 ) = τ (G). (b) Prove that for any DAG G there is a way to perform an add-one-

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step-by-step explanation:

hopefully im right

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation: