If A and B are subspaces of a vector space, then dim A < dimB, implies A is contained in B. Is this statement True? I think that the statement is true but NO.
Can someone state the reason, Please.

$L(\vec i$x$\vec j)$ and $L(\vec k)$ are both subspaces of $L(\vec i$x$\vec j$x$\vec k)$ and $L(\vec k)$ is not contained in $L(\vec i$x$\vec j)$
