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Let W, and W2 be subspaces of a vector space V. Prove that W

Chapter 1, Problem 19

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QUESTION:

Let W, and W2 be subspaces of a vector space V. Prove that W| U W2 is a subspace of V if and only if W, C W2 or W2 C W,.

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QUESTION:

Let W, and W2 be subspaces of a vector space V. Prove that W| U W2 is a subspace of V if and only if W, C W2 or W2 C W,.

ANSWER:

Step 1 of 3

From the given it implies that  or , then:

Thus,  and  are subspaces of ,

Then,  is also a subspace of .

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