prove that one and only one out of x,x+2 and x+4 is divisible by 3
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It's obvious.
i)Let x is divisible by 3 then x+2 is increased by 2 from x so it will have remainder 2.
again similarly x+4 have remainder 4
ii)if x+2 is divisible by 3 then x+4,which is 2 greater than x+2 wil have 2 as remainder and x,which is 2 less than x+2 will have 1 as remainder
iii)if x+4 is divisible by 3 then x+2,which is 2 less than x+4 will have 1 as remainder and x,which is 2 4 less than x+4 will have 2 as remainder
we can also check this by taking example
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hope it will help you
i)Let x is divisible by 3 then x+2 is increased by 2 from x so it will have remainder 2.
again similarly x+4 have remainder 4
ii)if x+2 is divisible by 3 then x+4,which is 2 greater than x+2 wil have 2 as remainder and x,which is 2 less than x+2 will have 1 as remainder
iii)if x+4 is divisible by 3 then x+2,which is 2 less than x+4 will have 1 as remainder and x,which is 2 4 less than x+4 will have 2 as remainder
we can also check this by taking example
------------------------
_______________
hope it will help you
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