Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer
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QUESTION :-
Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
SOLUTION :-
Let a be any positive integer and b = 2. Then by division algorithm, a = 2q + r, for some integer q > 0, and r = 0 or r = 1.
Because 0 < r < 2. So, a = 2q or 2q + 1
If a is of the form 2q, then a is an even integer. Also, a positive integer can be either even or odd. Therefore any positive odd integer is of the form 2q + 1
Answered by
1
Let ,
a = positive integer
b = 2
By division algorithm
a= 2q+r
q is greater than or equal to r
so,
a = 2q or 2q+1
If is the form of to give the knees knees and even integer also a positive integer can be either even or there for any positive integer is of the form of 2q+1
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