00:04
Okay, we have these combinations, right? propositions with statements and putting them together.
00:10
Okay, so this is just going to be, right? we're going to use p, q, and r.
00:17
And then we're going to use our symbols like and or, or, or not.
00:24
Right, like this is all that we're doing here is, oh, and then our implication, which is an arrow.
00:32
So we're just going to look at these and interpret them, right? so we said that p represents you get an a, q represents you do every exercise, and r, or sorry, p is you get an a on the final exam.
00:45
Q is you do every exercise, and r as you get an a in this class.
00:48
So we'll say you get an a in this class, but you do not do every exercise in this book.
00:53
Okay, so that means you do get an a, so i'm going to say, here's the answer to number a, which is you do it.
01:01
You get an a, which is p, but you do not do every exercise in the book.
01:05
P and not q.
01:08
P and not q.
01:11
You got an a and you did not do every exercise.
01:17
Let's move on to number b.
01:20
Now let's look at it, and it'll say, you get an a on the final, you do every exercise in this book, and you get an a in this class.
01:27
Okay, so you got an a in the class.
01:30
So that was r, r, and you do every exercise.
01:37
That would be q.
01:39
R and q, and you got an a on the final.
01:42
So that's and very good.
01:46
And that's it.
01:47
All right.
01:47
Now let's look at number c.
01:51
To get an a in this class, it is necessary for you to get an a on the final.
01:55
So this is necessary and sufficient, right? so we would say in an implication, if we have p implies, q, and that says that q is necessary for p.
02:11
Necessary for p.
02:12
That's n.
02:16
Necessary for p.
02:18
Q is necessary for p.
02:20
All right.
02:21
So that's how we're going to interpret it.
02:22
We're going to say to get an a.
02:23
It's necessary for you to get an a on the final.
02:26
So we would say to get an a in this class, which is r.
02:31
R.
02:32
It is necessary that the second one, what was it? it is necessary for.
02:36
For you to get an a on the final.
02:38
P, right? r implies p.
02:43
P is necessary for r.
02:46
P is necessary for r.
02:47
Those are just keywords.
02:48
That's really all it is...