I know that a graph G' is a subgraph for G if V(G')⊆V(G) and E(G')⊆E(G).
Today my professor wrote that G' is a subgraph for G if G' is a graph and V(G')⊆V(G), and then he told us that this definition is equivalent to the one we've seen before (= the first line in this post).
However, I don't think that these definitions are equivalent. In fact, if this is G:
2 / \ 1 3
and this is G':
1 - 3
we have that G' is a subgraph for G according to the second definition (wrong), while it is not according to the first one (right).
Am I missing something or was the professor wrong?