giniastiefel
giniastiefel giniastiefel
  • 17-09-2018
  • Mathematics
contestada

what is a counterexample for if (a-1)(1-b)=0, then a=b=1

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jimthompson5910 jimthompson5910
  • 17-09-2018

If a = 1, then a-1 = 1-1 = 0 and we can say (a-1)*(1-b) = 0*(1-b) = 0. This statement would be true no matter what value we pick for b. We don't have to make b = 1 true. We can say b = 2 for instance and have...

(a-1)*(1-b) = (1-1)*(1-2) = 0*(-1) = 0

and we get the same result 0. We can flip things around and make b = 1 while 'a' is any number we want (and it doesn't have to be 1)

So in short, either a = 1 or b = 1 or both are 1 and the entire equation would be true.

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