Question

For some positive integer m, every positive even integer is of the form

(a) m − 1
(b) m + 1
(c) 2m
(d) 2m + 1

Answer 1

(c) 2m

Every positive even integer is in the form of 2m.
Proof:
Let m be a positive even integer.
On dividing m by 2, let q be the quotient and r be the remainder.
∴ m = 2q + r, where 0 ≤ r ≤ 2
⇒ m = 2q + r, where r = 0,1
⇒ m = 2q and m = 2q + 1
But,
m = 2q + 1 = odd
∴ m = 2q = even