I need help with this problem. With the remote learning I am having a hard time understanding the problem. Follow the hint if possible. Please explain your reasoning and show all work. Thank you.

Using strong induction, prove that if G is a simple graph with n vertices, & connected components, and no cycles, then G has n - k edges. Note: Remember to use build-down induction! This induction proof requires a proof on two variables. Define the predicate P(n, k) where n 2 / and in the inductive step show that both P(i + 1, j) and P(i, j + 1) are true (an increment on both variable independently!). Hint: If the connected components have no cycles, what must they be