Given that x and y are positive integers such that (x+y) is an odd number, show that (x+3y) is an odd number and state your reasoning clearly.
Please answer the following question.
x and y are positive integers.
thus, y = 2m for some positive integer m
(x+y) is odd number
so, x+y = 2n +1 for some n in N.
x+3y = x+y+2y
n and m are positive integers, hence n+m is also a positive integer say k
x+3y = 2k+1
hence, x+3y is odd number.
Show that every positive even integer is of the form2q and every positive odd
integer is of the form 2q +1where q is some integer.