00:03
All right, so on our question here it says, the following arguments are all valid.
00:06
Give the informal proofs of these arguments.
00:08
So for this first one, it says b is small unless it's a cube.
00:12
If c is small, then neither or either d or e is too.
00:17
If d is small, then c is not.
00:19
If b is a cube, then e is not small.
00:21
If c is small, then so is b.
00:23
So our breakdown for that would be here.
00:28
Assume that c is small.
00:29
We want to prove that b is small.
00:31
Assume by way of contradiction that b is not small.
00:33
Then by the first premise, b is a cube.
00:36
Then by the final premise, e is not small.
00:39
But then by the second premise, d is small.
00:41
But the third premise assures that if d is small, then c isn't contradicting our initial assumption...