show that every positive even integer is of the form of 2 q and that every positive odd integer is of the form of 2 q + 1 where q is some integer
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Step-by-step explanation:
let a be any positive integer where b=2
according Euclid's division lemma
a=bq+r where
r=0,1
substituting the values of r in the above statement
a=2q+0
a=2q(it is a positive even integer)
a=2q+1
=2q+1(1 added to any positive even integer is a odd number)
therefore,every positive even integer is of the form 2q & every positive odd integer is of the form 2q+1.
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