I have the following problem where I am asked to construct a family of trees (one for each $n$) that have exactly 2 leaves.
I am having difficulty with this problem mainly because I cannot find a definition for the phrase "family of trees". I have searched online and through Rosen's 7th edition of Discrete Mathematics and have come up empty handed. If someone could please provide a definition and perhaps a source, I would appreciate it.
It’s not a technical term; that’s why you don’t find a definition. Set or collection could be substituted for family without changing the meaning.
You’re being asked to show that for each $n$ (each $n\ge\text{something}$?) there is a tree (of height $n$? with $n$ vertices?) that has exactly $2$ leaves. The nicest way is to give a general construction that takes $n$ as input and produces the desired tree. (In fact the term family may have been chosen to push you in that direction, since it suggests a collection of things that are somehow naturally related.)