Let $V$ be a finite-dimensional vector space and let $A$, $B$ and $C$ be subspaces of $V$. Which of the following statements are true?
(a) $$A \cap (B + C) = (A \cap B) + (A \cap C)$$
(b) $$A \cap (B + C) \subset (A \cap B) + (A \cap C)$$
(c) $$A \cap (B + C) \supset (A \cap B) + (A \cap C)$$
My attempt:
I was drawing the Venn diagram. From Venn diagram I concluded that
$$A \cap (B + C) = (A \cap B) + (A \cap C)$$ is true ..
Is my answer is correct or not, im not sure about my answer help Me..
Best Answer
In fact, it is only choice c which is correct.
As a counter-example for the other two, consider the following: