1. The problem statement, all variables and given/known data Let U, W be subspaces of a vector space V. Show that dim(U+W) = dim(U) + dim (W) - dim (U intersect W). 2. Relevant equations 3. The attempt at a solution I can see this picture-wise in a venn-diagram form. In adding U and W you count the elements in their intersection twice, since both spaces contain them. Thus, you subtract the dimension of U intersect W. But, how do you show this in proof format? It doesn't seem like a verbal explanation is enough.