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
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-> 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
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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(52784) (Show Source):
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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