Exercise 2. Let G be a graph and let a and b E G such that d(a) = A(G) and d(b) = 8(G) ≥ 1. Suppose that b is the unique vertex in G such that d(b) = 8(G). Define the following two sets: A = {ve G: d(v) < d(u) u € N(v)} B = {veG: d(v) > d(u) \ u € N(v)} (1) Show that a & A. (2) Show that A is a stable set. (3) Suppose that G is a bipartite graph such that G = G(A, B). Show that G contains an even cycle. (4) Suppose that A = {₁, ₂,..., us} and B = {v₁, V₁,..., Us} such that uv; E E(G) V s. Show that AUB V(G).

The sum of the squares of two numbers is 400 and the difference is 4.Use DNE if the answer Does Not Exist. Find the numbers. The larger number is    .The smaller number is    .

It costs $60 to buy green bean seeds. Green beans sell for $40. It takes 10 days for green beans to grow however, after the first harvest, the green bean plant will regrow in 3 days to be harvested again. For one green bean plant, how many dollars can you make per day?

A total of $6000 is invested for 5 yr with a total return of $1080. Part of the money is invested in a fund that returns the equivalent of 2% simple interest. The rest of the money is invested at 4% simple interest. Determine the amount invested in each account.