Question

Q&/3) = {a + b3 + c^9: a,b,c € Q} QUESTION 4 Which of the following rings R. is S a subring of R? O R = set of integers, S = set of odd integers. OR is the set of integers, and S = 6Z R is the set of complex numbers, and 5 = {a + bi: a, b E ZH R= Z125Z, and S = {0,5,10,15,20). QUESTION 5 Which of the following rings R, is S an ideal of R? OR= set of integers, S = set of odd integers. R is the set of integers, and S = 6Z R is the set of complex numbers, and 5 = {a + bi: a, b EZ} OR=Z/25Z, and S = {0.5,10,15,20). Click Save and Submit to save and submit. Click Save All Answers to save all answers.

select all that apply please

Answer 1

Solution Roy Rings, S-> Subring or R Ra set of integers S set of old integess false -) R (24) is nina By subring definition 1,36S 1-3-245 -) Sis not subring of R. R is the set of integess, and s: 62 true Vat GZ, Vb+62-7 a-be 67 r at82, v beth a a. bt67 (1) R is the set of complex numbers, and solathi , a, b123 frue s) R=( Q,+,.) is ring, V at bid es, v Q4+ bedes ) (91-92)+(bir be gats & qutblits W Olet boits al (9, +hi) (9,7 bzi) =) sis subring of R. 19, 92 - by b2 )+ (by9z+9, 62) ES R = 7/a57 10,5,10,15 120) ( and true (57) bring and (1) Vars O vaes, Abas v brs a arbes -) 9.be S. s is subring of R.

Pinswer 6 R = rings s. ideal of R. - D R = set of integers , se set of odd integers. false R = (2,+, .) is ring. O IES By ideal definition 3S -) 1-3=-343 TES QER -) 8.1=245 s is not ideal of R. R is the set of integess, and S=62: true 9.bfs R=(2,+,-) is ring Check ideal ats v bts a) 9.7 eS H965,VBER and goats s is ideal of R. R is the set of complex numbers, and so farba ; a, bf 2] Ra (Pita) is ring check ideal. 9, +by ES Vaqtbui fs =) (94-92)+ (by-bz) its tits and F2 fr ) 2. (1+i)= {2+ hits so not ideal of R. & False R=7%252and set 0,5,10,15, 20) trul E King R= 7/a52 Check incolo o & aes, v bts = a-b es NER grafs 1 augas s is ideal of R.