00:03
All right, i am supposed to determine the truth value for a couple of different statements here, for some very specific values for p and q and r.
00:13
So i've just got one line of a truth table written out here.
00:17
You can fill in p is false, q is true, and r is false.
00:25
Using these original truth values to evaluate this much more complicated statement.
00:31
All right, so to evaluate our big statement here, i'm going to do the same thing as i do in algebra class and start with my parentheses.
00:42
I'm looking at the combination of p and not q.
00:45
Those are being combined with a conjunction and before i can combine p and not q, i need some truth values for not q.
00:56
So i'm going to start with that, not q or the negation of q simply has the opposite truth value.
01:02
Of q.
01:05
Looking at my original truth value for q is true, that the instigation of q is false.
01:12
Now i can put q together with p using the conjunction and i'm wondering the statement p and not q is that true.
01:23
P and not q is true if both statements are true.
01:28
So the conjunction and requires both components to be true in order for the conjunction to be true.
01:35
Looking back at p and not q, are they both true? no.
01:43
False.
01:44
Neither one of those actually are true.
01:46
So not even close.
01:49
All right, but actually i want the negation of that.
01:54
So i've evaluated the quantity, p and not q, but i want to negate that or actually take the opposite of that statement.
02:05
All right.
02:06
So the value for p and not q is false.
02:09
Meaning the negation of that will be true.
02:14
And now i can look at how that relates when we use the implication with r.
02:20
So implication is an if -then statement.
02:24
If the first statement is true, then the second statement should also be true.
02:33
So if p and not q is true, then r is also true.
02:39
All right.
02:40
Well, let's take a look at the truth of that.
02:43
The order is important here.
02:45
So i'm going to start with my first statement, the negation of p and not q.
02:52
Yep, that is true.
02:54
And if that is true, then r is supposed to also be true, but it's not.
03:01
So our implication is false.
03:04
And that's actually the only way to goof up and make an implication false is if the first statement is, true and then the second statement is false, then your implication will be false.
03:20
Otherwise, it's actually always true.
03:23
So that completes the evaluation of this statement.
03:27
Our implication of the negation of p and not q implies r that is false.
03:37
Okay, now we can move on to the second statement here...