00:01
Okay, i want to work out which of the three are a tautology and the three here are in different colours.
00:09
I'll go through it one by one.
00:12
Start off with r and q as usual.
00:15
T t, t, ft, ft, f f f, on the left here.
00:20
There are the four possible outcomes for each statement.
00:23
True or false.
00:25
And let's begin off then with this one here, which is going to be r and k.
00:31
Well this and connective is only true if they're both true so this one will be true t t f is false ft is false so with this connective and you must have both items true to be true overall now we then have r or r and q so it's going to be this one with this one joined by the or connective and with or if you have one true or two truths the overall statement is true so if you see one t it's true the first one then what we have is t and t that's true here we have t and f so true but here though is f and f f they're both false what i have then here is t, t, t, f, f.
01:46
So it's not going to be a tautology in this case.
01:50
So here the answer is no for that one.
01:53
Okay, that's the first one done.
01:55
That's a, so a the answer is no.
01:58
Let's do b now.
02:00
The first column is not r.
02:03
Well, r is t -t -f -f, so not r must be f, f -t, the reverse of r.
02:10
Here i have q and not r.
02:14
So i take this column with this column and join with and.
02:22
Again for and i must have two t's to be true.
02:26
So the first one is tf not going to work.
02:29
Tf not going to work.
02:30
T t is going to work.
02:32
Ft won't work.
02:34
I have f here...