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. Let R be a ring and S,T subrings of R. In each of the following cases, provide a proof if the answer is yes, and provide a counterexample if the answer is no. (a) Is S∩T a subring of R ?

User JoeKir
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Final answer:

Yes, S∩T is a subring of R. The statement about the electric field requires more information.

Step-by-step explanation:

In the case of (a), if S and T are subrings of R, then S∩T is also a subring of R. To prove this, we can use the subring test, which states that for S∩T to be a subring of R, it must satisfy three conditions: (1) it is closed under addition, (2) it is closed under multiplication, and (3) it contains the additive identity of R. Since S and T are both subrings of R, they already satisfy these conditions, so S∩T will also satisfy them and therefore be a subring of R.

In the case of (d), the statement that there is a point between S and T where the electric field is zero depends on the specific situation being considered. Without more information, it is not possible to determine the truth of this statement.

User Tenzin Chemi
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