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Studying for abstract algebra and real analysis finals for tomorrow then I'm graduated!: Mo San h Abatrac Thoma Inter #UN 5OVERET MATH 432 Hahn LUNE (5 pts) at of your work. Do not make false statements. Keep your eyes Tost 1 (5 pts each) 1. Define a group < G, * >. m WITH SELECT TEAS AND NATURAL FLAVORS PLEAEE etermine if each of the following statements are true or false. If it is true Drove Crener prove it false or give a counter-example. (Hint. These are all false.) 3. (a) Every finite cyclic group has at most two generators. (B) If every proper subgroup of a group is cyclic, then the group is cychc. (c) Every finite group is abelian. (5 pts) 3. Given the following permutations, 2 3 4 5 6 7 8 5 6 8 :) 1 2 3 4 5 6 78 3 4 1 8 7 5 2 6 4 3 1 7 compute o OT, TOO and o-1. (10 pts each) 4. Determine if the following sets G with the given binary operations * are groups. If they are, veriEY Che axiomms. If they are not, explain which axioms fail. If it is a group, determine if it is abelian. (lf the operation is a usual form of multiplication or addition, you may assume associativity.) (a) Let G =R+ and let a * b= a. %3D (b) Let G = Z* and let be multiplication. (c) Let G = Z; and let be multiplication mod 7. (d) Let G = Un= {z € C|2" = 1} and let * be addition. |3D (e) Let G= {A € M2,2(R)I det(A) = 1}, and let * be matrix multiplication. (15 pts) R be defined by o(x) = 2x + 1. 5, Let o: R %3D (a) Show that o is a bijection. (b) Define the binary operation so that o:< R, * >→<R,+ > is an isomorphism. (c) What is the identity for ? 10 (10pts) (a) Let o: G G' be an isomorphism between two groups < G,*> and <G,>whose are e and e' respectively, and let H<G. Prove that oH <G'. 6. Choose one of the following problems to do. Clearly indicate which problem you wish to have g (b) Vet G be an abelian group. Prove that the set of all elements of G that are their ow Aorms a subgroup of G. What happens if G is not abelian? G be a group, and let H <G. Define a relation on G by a~bif and on 7. 2) n equivalence relation on G. Ind by a, and let o:G G be an isomorphi Tea Made Wien Real Brewed TWISTED TE HARD ICED TEA ORIGINAL Studying for abstract algebra and real analysis finals for tomorrow then I'm graduated!

Studying for abstract algebra and real analysis finals for tomorrow then I'm graduated!

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This sub is soooo toxic and sexist. I found a recent post of these people just assuming that this girl with a kid on tinder is a “slut”. I can smell the virginity through my screen just scrolling through this: 1:31 LTE O Q r/WhereAreAllTheGoodMen r/WhereAreAIITheGoodMen + JOIN 43,941 members • 324 online In response to r/niceguys, this sub is dedicated to exposing all the women who complain about wanting a "good man", to show what happens when women reject decent men for jerks and promiscuity, along with showing the unreasonable standards women have while offering little to no value themselves. Show Less Explore Posts About 1 TOP POSTS TODAY - Or/WhereAreAlITheGoodMen Best of fi Top posts from the past month "I thought this g want me and no and I'm upset ab Child support payer wanted! requirements: as borderline sexual har Age 16-23 done my best to just pu establish boundaries an where I've felt I really ne it's got very close. I rece a girlfriend now. They've about a month but she's educated, apparently sh whipped, and he talks a greatest thing to ever h- not interested in this gu kind of upset about it. H Never used any prescription or illicit drugs Never drank except for communiunm Blonde or light brown hair, not overweight, and comes from a 75%+ American background Agrees to forfeit all parental rights at time of birth No payment will be collected during any natural "breeding" sessions, however regular child support payments in the amount of 20% of your income will be expected within the first month of birth. You will remain completely anonymous throughout the child's 18 years of life, and you would be expected to maintain that same level of anonymity with anyone around you. Please reach out to me through messenger for more information. Thank you! 1.1k points • 266 comments 1.1k points • 246 com u/Heypunk11 • 15h Who would have guess your actions have 534 This sub is soooo toxic and sexist. I found a recent post of these people just assuming that this girl with a kid on tinder is a “slut”. I can smell the virginity through my screen just scrolling through this

This sub is soooo toxic and sexist. I found a recent post of these people just assuming that this girl with a kid on tinder is a “slut”....

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