Problem 3

Let V be a vector space over F and suppose W₁ is a subspace of Vand W₂ is a subspace of V. (b) Find an example of a vector space V over a field F and two subspace W₁ and W₂of V such that W₁U W₂ is not a subspace of V. (Please provide a full justification that W₁U W₂ is not a subspace of V. \text { (a) Show that } W_{1} \cap W_{2} \text { is a subspace of } V \text {. }