00:01
Okay, we have here then three statements, pq and r.
00:03
That requires an eight -line truth table.
00:07
What we do always is the first column p is four t's, four fs, column q, two t's, two fs, two fs, all the way down.
00:17
The last column tf, tf, tf, tf, tf.
00:20
That pattern is a standard for these kind of problems.
00:26
First line, three t's, last line, three fs.
00:31
Now, we start off with this item here, q and r.
00:39
So we look at that column and that column.
00:44
Now, and requires two t's to be true.
00:48
You must have q true and r true at the same time.
00:51
So two t's only give you true, otherwise false.
00:55
So i see here i have two t's.
00:58
So it's true.
00:59
Here we have t f, so it's false.
01:02
Ft is false.
01:03
False ff is false t t is true tf is force and here is false and two fs would be false so just two t occurs twice the first column done then we deal with p implies q andr so we take this column with this column and for implies is always true unless you have tf.
01:39
So this symbol here, always true apart from tf.
01:46
Here i have t, t, t, so that must be true.
01:53
Here i have tf, so that must be false.
01:59
And what you do normally is look for the tf first all the way down, and here i see tf as false.
02:09
Here is t f and the rest are ft f f f f f f f f all the rest must be true so get the old ones out look for t f that's the force that one is the false one the rest are all true now that's that column complete so that our label star that's this item here now next i want to work out this bit here p implies q so i take p with q and again with implies only t f is false.
02:59
So look for tf in the first two columns.
03:03
So t t t f here is false.
03:08
T f here is false.
03:10
The rest are all f first.
03:12
So it must be true all the way down...