SET® Mathematics
Proof of Theorem 1.5

corner Sets

  Proof of the set 1,6,8:
 

 Cbc

Cc(ab)

Cac

Ca(bc)

Cc

Cb(ac)

Ca

Cab

Cb
  (bc)(ab) = b(ac) (bc)(ba) = b(ac) b(ac) = b(ac)

 

Proof of the set 3,4,8:
 

 Cbc

Cc(ab)

Cac

Ca(bc)

Cc

Cb(ac)

Ca

Cab

Cb
  (ac)(a(bc)) = ab a(c(bc)) = ab a(b) = ab

 

Proof of the set 7,2,6:
 

 Cbc

Cc(ab)

Cac

Ca(bc)

Cc

Cb(ac)

Ca

Cab

Cb
a(c(ab)) = b(ac) (b(ab))(c(ab)) = b(ac) (ab)(bc) = b(ac) b(ac) = b(ac)

 

Proof of the set 9,2,4:
 

 Cbc

Cc(ab)

Cac

Ca(bc)

Cc

Cb(ac)

Ca

Cab

Cb
  (b(c(ab)) = a(bc) (a(ab))(c(ab) = a(bc) (ac)(ab) = a(bc) a(bc) = a(bc)

 
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