00:01
Okay, i want to prove the first the morgan's rule.
00:04
So not brackets p and q equals not p or not q.
00:10
To do that is my truth table.
00:14
P and q, it's always t t, f f f f to begin with, four possible outcomes for p and q.
00:22
And i'll do first, not p.
00:25
Not p is the reverse of column p.
00:28
So t becomes f, t becomes f, f becomes f becomes t, f becomes t.
00:35
Then we do not q.
00:38
Let's reverse column q.
00:40
Instead of tf, tf, we do ft.
00:46
Now, i want to do left -hand side, so p and q first.
00:51
Let's do p and q.
00:54
So i take this column with this column, and the word or the conjunction here you have and.
01:06
And means you need two t's to be true.
01:10
So they both must be true for the whole thing to be true.
01:14
So t -t -t will be true.
01:17
T -f will be false.
01:19
F -t will be false.
01:21
And f -f will be false.
01:24
So the rule then for and two t's.
01:30
Then not p and q.
01:36
Let's reverse that column.
01:38
This column here, reverse it.
01:40
So t is f f f is t f is t f is t so that's the left -hand side then now the right -hand side is not p or not q so not p or not q so we take this column with this column and the rule for or is if you see one t or two t's overall it's going to be true it's either or or both so if one is true you're five the first one then we have f f.
02:19
So that one is going to be false.
02:22
Here i have ft.
02:24
Well, i see one t, so it's true.
02:27
Here is t .f.
02:29
Again, i see one t, so true.
02:32
And the last one, t, t is true.
02:35
Which means then these two things are the same because this true table here and the one here, they match up...