Prove that W is subspace of vector space V(F) iff x-y belongs to W and αx belongs to W

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A non-empty subset W of vector space is subspace of V iff αx+βy ∈ W for all α,β∈F and x,y∈W A non-empty subset W of vector space is subspace of V iff αx+βy ∈ W for all α,β∈F and x,y∈W
A non-empty subset W of a vector space V(F) is a subspace of V if and only if x+y ∈ W and α.x ∈ W. A non-empty subset W of a vector space V(F) is a subspace of V if and only if x+y ∈ W and α.x ∈ W.
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