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1. Check whether the following set F forms a ?eld with respect togiven operation

ID: 2937143 • Letter: 1

Question

1. Check whether the following set F forms a ?eld with respect togiven operations.


(a) F = {a + b2 R : a, b Q} considered asa a subset of R with respect to the usual operations of

addition and multiplication.


(b) F = {a + bi C : a, b, c Q} considered as a asubset of C with respect to the usual operations of

addition and multiplication.


(c) F = {a + b2 + c3 R : a, b, c Q} considered as a a subset of R with respect to the usualoperations

of addition and multiplication.


PLEASE PROVIDE PROOF. This was the hardest part forme. I can show isolated examples of instances that conform to afield but cannot prove it generally. If you are very good in thisarea, I have a few more questions that are similar including partsd. e. and f. of this same problem. I will post the question underthe same nickname. I WILL RATE LIFESAVER.


Thanks in advance, I hope someone can helpme.

Explanation / Answer

all the above three sets form a field. i have shown one of these to be a field in your previouspost.