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Assessed Question 5.15. Decide whether each of the following statements is true or not and briefly prove your claim (a) Let c
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a) True We will use the followana th eorem A non-emphy subset s of a ving R. is a subring stwe show that S is a subset of R kouw, to pwve S is a subnną of R we need to ohow a-bes and ab eS For «ll a,b Es yictzıc2 where 지, 2 -X2-у, е г.С os an elementGiven c=5 SinCe So, note that c3_%) 3+1So since z is closed under addihiom and multiplica- се und єї tion we have, z s) Zl So, a-b S Hence, S te a subring of R

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