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Not sure how solid this is but heres what I thought:
You were right in that this seems to scream reductio ad absurdum. You have an upper bound for the size of the edge set (3 since we can't have cycles in a tree) so if you show that you have enumerated all of the possibilities smaller than three you say: assume there is another forest then we need either another vertex (which we don't have) or another edge which cannot be the case since this would give a cycle in any other graph of 4 verticies (essentially this would violate the relation for trees: |E| = |V| - 1).
You were right in that this seems to scream reductio ad absurdum. You have an upper bound for the size of the edge set (3 since we can't have cycles in a tree) so if you show that you have enumerated all of the possibilities smaller than three you say: assume there is another forest then we need either another vertex (which we don't have) or another edge which cannot be the case since this would give a cycle in any other graph of 4 verticies (essentially this would violate the relation for trees: |E| = |V| - 1).
Draw all graphs on 4 vertices. Pick out the ones that are forests.
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