Is there something incorrect in this question?

Question

Let G be a bipartite graph with two Groups A, B. Given: |A| =2, |B|=n and that there are edges that connect every single node in A with every node in B. Let T be a spanning tree of G, Prove that There is a node in B such that it's connected to both nodes in Group A in T.

Why this is even true? I could take t to include 0 edges which says that the above claim is totally wrong.

Answer 1

Let $A=\{a_1, a_2\}.$ For $k=1,2$, let $B_k$ be the vertices of $B$ that are joined to $a_k$ in $T.$ Once you explain why the intersection of $B_1$ and $B_2$ can't be empty, you're done. (In particular, each $B_k$ is nonempty.)

Answer 2

For $T$ to be a spanning tree, there must be a path in $T$ from one of the vertices in Group A to the other one. Think about what such a path must be.