00:01
We want to prove if x is in z, then x is even if and only if 3x plus 5 is odd.
00:09
So to go in this direction, assume x is even.
00:19
So therefore, we can write x as 2 times some integer n.
00:29
So then let's calculate this.
00:32
So 3x plus 5 comes out to be 3 times 2n plus 5.
00:44
And that's equal to 6n plus 5.
00:48
So the first term there is always going to be even no matter what the value of n is.
00:53
And we add an odd number.
00:58
And so what we're left with is odd.
01:01
And so going in that direction, we see it like that.
01:04
To go the other direction, there's a couple ways we could do this.
01:10
We could assume that x is odd and find out what happens, which is probably the easier way to do it...