The given statement is false..
The reason being :
a) A spanning tree is a subgraph of a graph such that it covers all the vertices..
b) Contains (n-1) edges given n vertices..
Now consider a subgraph of n' vertices where n' < n such that the resulting subgraph is acyclic..Now this is a valid tree but not a spanning tree as it violates a) point..
Hence the given statement is false..