This is not a tree since it contains a cycle. Note also that there are too many edges to be a tree, since we know that all trees with \(v\) vertices have \(v-1\) edges.

This is a tree since it is connected and contains no cycles (which you can see by drawing the graph). All paths are trees.

This is a tree since it is connected and contains no cycles (draw the graph). All stars are trees.

This is a not a tree since it is not connected. Note that there are not enough edges to be a tree.