We've done questions a bit like this before, but nothing with subspaces. Basically, for a vector space V there exist subspaces X, Y and Z in V (with dim V > 1), determine, either by proof or counter-example, whether the following statements are true or false:

$\displaystyle

X + \left( {Y \cap Z} \right) = \left( {X + Y} \right) \cap \left( {X + Z} \right)

$

and

$\displaystyle

X \cap \left( {Y + \left( {X \cap Z} \right)} \right) = \left( {X \cap Y} \right) + \left( {X \cap Z} \right)

$

Help?!