Question

show that every positive even integer of the form 2q and that every positive odd integer is the four 2q + 1 for some integer q.​

Answer 1

Answer:

Very easy by taking examples

Step-by-step explanation:

Let s take q=3

2q=6. (even)

2q+1=7 (odd)

Answer 2

Let n be the arbitrary postive integer on dividing n by2 we get q as quotient and r as remainder

Then by euclid division lemma we get

n= 2q+r where 0=<r>2

when r=0

n=2q

When r=1

n=2q+r

2q+1

here 2q is clearly even

and 2q+1 is odd

Hence every positive integer can be express in the form of 2q or2q+1