Question

Show that every positive even integer is of the form 2q & that every positive odd integer is of the form 2q + 1, where q is some integer.​

Answer 1

Question:

Show that every positive even integer is of the form 2q & that every positive odd integer is of the form 2q + 1, where q is some integer.

Solution:

Euclid's divison lemma

→ a = bq + r

→ a = 2q + r 【where r = 0, 1】

• If a is even number then, r = 0.

→ a = 2q + 0

→ a = 2q

• If a is odd number then, r = 1

→ a = 2q + 1