Solved: Recall that the intersection of two sets W1 and W2 is the set of all elements
Chapter 7, Problem 52(choose chapter or problem)
Recall that the intersection of two sets \(W_1\) and \(W_2\) is the set of all elements common to both sets, and the union of \(W_1\) and \(W_2\) is the set of elements that are in either \(W_1\) or \(W_2\). Suppose \(W_1\) and \(W_2\) are subspaces of a vector space V. Prove, or disprove by counterexample, the following propositions:
(a) \(W_{1} \cap W_{2}\) is a subspace of V.
(b) \(W_{1} \cup W_{2}\) is a subspace of V.
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