Let S,T be subspaces of the vector spaces V ,U (respectively), and let

$\displaystyle T : V × U -> (V/S)× (U/T)$ be the linear map defined by $\displaystyle T(x, y) = (x +S, y + T).$ Find the kernel of T and prove that

$\displaystyle (V× U)/(S× T) (~ =) (V/S) × (W/T).$

Plx help...