SOLUTION: Let Ω ={ω∈Z|ω= 8x+ 1, for some x∈Z} and A={α∈Z|α= 8y−7, for some y∈Z}. Using element argument, prove that Ω =A

Question 1166867: Let Ω ={ω∈Z|ω= 8x+ 1, for some x∈Z} and A={α∈Z|α= 8y−7, for some y∈Z}. Using element argument, prove that Ω =A
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.

It can be justified differently.

One way is to notice that both sets represent all integer numbers that give the remainder 1 when are divided by 8.




The other way is to notice that 


    if  ω = 8x+1 belongs to one set, then the same number 

        ω = 8x+1 = 8*(x+1)-7 belongs to the other set,

    and vice versa.


It means that the two sets COINCIDE.

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Solved, completed and explained.

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