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If A=[{:(1,2),(4,1),(5,6):}] and B=[{:(1...

If `A=[{:(1,2),(4,1),(5,6):}]` and `B=[{:(1,2),(6,4),(7,3):}]`, then varify that (i) (A-B)'=A'-B'

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We have, `A=[{:(1,2),(4,1),(5,6):}]` and `B=[{:(1,2),( 6,4),(7,3):}]`
(i ) `therefore (2A+B)=[{:(2,4),( 8,2),(10,12):}]+[{:(1,2),(6,4),(7,3):}]=[{:(3,6),(14,6),(17,15):}]`
and `(2A+B)=[{:(3,14,17),(6,6,15):}]`
Also, `2A+B=2[{:( 1,4,5),(2,1,6):} ]+ [{:( 1,6,7),(6,6, 15):}]=(2A+B)`
(ii) (A-B)`=[{:(1,2),(4,1),(5, 6):}]-[{:(1,2),(6,4),(7,3):}]=[{:(0,0),(-2 ,- 3):}]`
and ` (A-B)=[{:(0,-2,-2),(0,-3 ,-3):}]`
Also `A'=B' = [{:(1,4,5),(2 ,1,6):}]-[{:(1,6,7),(2,4,3):}]`
`=[{:(0,-2,-2),(0,-3,3):}]`
=(A-B)'
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