Question

show that every positive even integer is of the form 2q and that every odd positive integer is of the form 2q+1, where q is some integer

Answer 1

Here u go


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Answer 2

Answer:

Step-by-step explanation:

1. Let a be any positive integer and b=2. Then, by Euclid's division lemma there exist integers q and r such that

a = 2q + r , where 0 </= r < 2

now, 0 </= r <2

=> 0</= r</= 1

=> r=0 or, r=1 ( because r is an integer)

therefore a =2 q, then a is an even integer.

we know that an integer can either be even or odd. Therefore any odd integer is of the form 2q +1.