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(a) For any a: E F, (1)'a: (Hint: It is enough to prove that :L' +(1)o:c = 0.) (b) If$,yF, andx-y=0,then$=00ry: (c) Ifx,y,zF,and33+z=y+z,thenx=y.

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Q: Let F be a field. Prove the following statements. Justify each step in your proofs, and make sure to use only the field axioms, or claims that have been already proved.

Screen Shot 2018-06-04 at 2.51.11 PM.png

Screen Shot 2018-06-04 at 2.51.11 PM.png

(a) For any a: E F, (—1)'a: = —:z:. (Hint: It is enough to prove that :L' +(—1)o:c = 0.)
(b) If$,y€F, andx-y=0,then$=00ry:0. (c) Ifx,y,z€F,and33+z=y+z,thenx=y.

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