00:01
Okay, the first one here we have p by implies not not p.
00:05
Well, not not p is simply p.
00:08
So if p by implies p clearly that is always going to be true, so that will be a tautology.
00:18
If p then p both ways, always true.
00:24
The next one is p and not p.
00:30
Well, we can't have p and not p at the same time.
00:32
You can have p being both true and false not possible so this one here must be a contradiction for a truth table you can have tf or ft and clearly that is not going to be true overall always false as c p or not p that one is always true either you can say p is true or p is not true either or so here must be a tautology.
01:19
Okay, next one we have this.
01:21
So here, let's draw a truth table for this.
01:24
What we have is p and q.
01:29
The four possible situations.
01:31
T, t, f, t, f, t, f, and f.
01:37
The first one, p and q, or and is only true if we have two t's.
01:43
So t here, these are all the f.
01:46
Then not p is the reverse of p so it's f f t not q the reverse of q so f t f t and then not p and not q i join up this column here this column here using and i need two t to be true so here is f t f t so here is f f f f f f f and here i have two t, so it's true.
02:20
And the last column we need is p and q, or not p and not q.
02:30
In other words, what i want, this column, combined with this column using or.
02:35
And with or, one t or two t's makes it true.
02:41
So the first one is t .f, that's true.
02:45
F, f is false.
02:48
F f is false.
02:52
T is true.
02:54
So this one then is neither.
02:57
I don't see all t's.
02:59
I don't see all fs.
03:00
So neither is the answer.
03:07
Okay the last one...