- #1
flon
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Hey guys this is the question
. Let A and B be vector subspaces of a vector space V .
The intersection of A and B, A ∩ B, is the set {x ∈ V | x ∈ A and x ∈ B}.
The union of A and B, A ∪ B, is the set {x ∈ V | x ∈ A or x ∈ B}.
a) Determine whether or not A ∩ B is a vector subspace of V . Prove your answer.
b) Determine whether or not A ∪ B is a vector subspace of V . Prove your answer.
My strategy for this is to find two subspaces in V and find a counter claim so that the union of A and B is not a subspace and similarly for the intersection of A and B would this be strategy be enough to answer the question?
thanks so much.
. Let A and B be vector subspaces of a vector space V .
The intersection of A and B, A ∩ B, is the set {x ∈ V | x ∈ A and x ∈ B}.
The union of A and B, A ∪ B, is the set {x ∈ V | x ∈ A or x ∈ B}.
a) Determine whether or not A ∩ B is a vector subspace of V . Prove your answer.
b) Determine whether or not A ∪ B is a vector subspace of V . Prove your answer.
My strategy for this is to find two subspaces in V and find a counter claim so that the union of A and B is not a subspace and similarly for the intersection of A and B would this be strategy be enough to answer the question?
thanks so much.