- #1

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- 1

- TL;DR Summary
- Problem is shown in the image

I included this image because it is easier than typing it out. Anyway, this is an old problem I need to catch up on. I have a clue as to how to do part a. I could say given an x that is a member of ∩V(A

_{i}) which implies that x is a member of V(A

_{i}) for ∀i. Then we can say ∀i all polynomials are in A

_{i}when the polynomial is equal to zero at x. Apparently this statement is the same as V of the union of A

_{i}. Still a little hazy on that. I don't know how to show the converse is true (which would prove the equivalency). This problem has me quite lost. But I suspect (b), (c), and (d) follow nicely from understanding (a). Any help is greatly appreciated. Thanks!