false! counter-example: obviously because
now see that but hence the equality does not hold.
true by modular law.
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:
and
Help?!
false! counter-example: obviously because
now see that but hence the equality does not hold.
true by modular law.