Question

Show and explain your work 5. (17 points) Identify the points) Identify the flaw in the proposed proof of the following red lowing result and how would you fix it. Remark. For every three sets, A. B. and C son (AXC) (BxC)C(AB) x C. Proof. Leti,y) E (A it follows that IE A y E (AXC)-(BXC). Then (r.) E AXC and (w & BXC Since (1.1) E (A - B) XC that I e A and ye C. Since (1) BXC, we have re B. Thus re e (x,y) EAC , XE A YEC, so cxente care bene e xeo IP Joc was already eam bitheat, since is folland # B <c Sincer, 4) | C. B. Thus re - B. Hence since (x,y) JE (AB)xc. Then xol and yet B since yt AB, it follor a AXC sinceto, hower and of BB/ xoc and yon, we have Cam c o Brc Therefore, Cry) E CANC-rech. Hence cAxe)-(BAC) & Bleccare)-(Brc) we now show that (Axc-cRxclsce sxC Then cr,y) + Axe and (x,y) € Bxc since the Axc, it follows that you kis since xcc and (x,y) e excit follows that yo B.So y t a xry) ECA-B) x C and (AXC)-(Bxc) ECA-B) xC ... sa cr xC let caye (Arc)-rex llows that cc and yot.. (1 .

Please help me understand where the flaw is and how to fix it in the given proof. I didn't get full credit.

Answer 1

CLASSTIME Page No. Date Solution. The flaw in the proof us : (x4) & BX C , we have x&B Sunce Correct let Then Proof (44) € (AXC) - (BXC) (x, y) E AXC and (ngY) & BX NOW (x,y) € AXC XE A and Y EL * And L * (24) & BXC either x4 B or y¢ C Correction of flow in the Proposed Proof I But L we know . We must that have yEC that x et B mus, we have that NEA, X4B and Y EC & XE A - B and y EC , (2,4) E (A - B) XC Hence (AXC) -/B XC) < (A-6) XC

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