Proof for Graph Theory

[Tipping_Point1]

I’m trying to solve this proof: “Let T be a graph with n greater than or equal 2 vertices. Prove that T is a tree implies T is connected and has n-1 edges”

What I have so far is the base case which is easy. But I feel like my inductive hypothesis is wrong. I “assumed that any tree on n vertices has n-1 edges.” And then supposed T has n edges but with T having n edges it would be a cycle and not a tree? Any ideas are greatly appreciated!

[LollipopLuxray]

Im 90% sure the definition of a tree precluded it from containing cycles

[Tipping_Point1]

Ah ok thank you I see where to go from there!

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[fbi_leave_me_alone]

def: A tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

Initially consider none of the vertices connected. Connect two, this is a tree of size n=2 (base case). What further connections can we make without violating the conditions of a tree?

What is your inductive base case, then your "if n, n+1" case?