Question

show that (if 5n+3 is odd then n is even :n is a natural number)

Answer 1

you can actually prove this using direct proof

Answer 2

first, assume 5n + 3 is odd

so 5n + 3 = 2k + 1

agree?

Answer 3

http://www.youtube.com/watch?v=ILdBDOPoEDQ

Answer 4

well there'd be an alternative :

5n+3 = 2(2n+1) +n+1

now, 2(2n +1) is always even no matter what natural number n is

only n+1 makes the difference

clearly,in n+1 = 2k ,then whole no. is even
and if n+1 = 2k +1 , then whole no. is odd

we are looking for odd,,
i.e. n+1 = 2k+1
or n = 2k
i.e. n is even..

hope that was good enough,,