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Question

If A=123579211 and B=415120131, then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'


Solution

(i)Here, A+B=123579211+415120131=532699142
(A+B)=561394292.....(i)
Also A+B=123579211+415120131=152271391+411123501=561394292........(ii)
From Eqs.(i)and (ii), it is verified that (A+B)'=A'+B'.

Here, AB=123579211415120131

=1+4213+5517290211311=318459320
(AB)=343152890.....(i)
Also, AB=152271391411123501=1+451212172133(5)9011343152890.............(ii)
From Eqs.(i)and (ii), it is verified that (A-B)'=A'-B'.

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