Consider the statement "every non trivial tree has exactly two leaves". The following is an attempted proof of the statement using induction on n, where n the number of vertices. Base case: n=2. The tree is a path, and has exactly two leaves. Inductive hypothesis: Assume that every tree on k vertices has exactly two leaves. Inductive step: Consider a tree T on k vertices. It has exactly two leaves. Add a vertex, make the new vertex adjacent to a leaf of T. Now the new tree has k+1 vertices, and has exactly two leaves. What is wrong with the proof?

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave

Select the number of ways in which a line and a circle can intersect

Which statement accurately describes how to perform a 90° clockwise rotation of point a (1,4) around the origin?