Suppose $\displaystyle U_1$ and $\displaystyle U_2$ be subspaces of a vector space V. Define the sum of $\displaystyle U_1+U_2$ as follows:

$\displaystyle U_1+U_2$ = {$\displaystyle u_1+u_2$: $\displaystyle u_1$ is an element of $\displaystyle U_1$, $\displaystyle u_2$ is an element of $\displaystyle U_2$}

1. Prove that $\displaystyle U_1+U_2$ is a subspace of V.

2. Let W be a subspace of V such that $\displaystyle U_1$ subset or equal to W and $\displaystyle U_2$ subset or equal to W. Prove that $\displaystyle U_1+U_2$ subset or equal to W

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