00:01
So this question is asking us to translate each statement into a logical expression, and we're going to do this using predicates, quantifiers, and logical connectives.
00:11
So what i'm going to do is i'm first going to go over the problem, each aspect of it, and then i'm going to go through each solution.
00:18
And then once i've written down each solution, i'll go ahead and go back and explain the logic.
00:23
So the problem states that the domain consists of all people.
00:29
So that means that x in this case is all people.
00:33
And then we go ahead and we get two proposition functions.
00:37
So those are going to be your p of x and your f of x.
00:41
So like i said, the domain is all people, also known as x, is all people.
00:52
And then our proposition functions are p of x.
01:03
What was it? go ahead and use equal signs actually.
01:05
And that means, oopsies, x is perfect.
01:14
And remember, our domain is all people.
01:17
So that means all people are perfect.
01:20
And f of x, which means x is your friend.
01:31
And then we're going to be using a few symbols that i'm going to just quickly go over.
01:35
So we're going to be using this symbol to mean for all.
01:40
We're going to be using this symbol, which is equal to not, or it's the negating symbol.
01:50
We're going to be using this for and.
01:57
We're going to be using this for or.
02:02
And we're going to be using the arrow to mean implies.
02:08
Implies, or you can think of it as implicates if then, those kinds of things.
02:18
So now let's go ahead and go over the answers for each one.
02:22
And i'm just going to label them one through six.
02:26
Now there is a bank for all of this.
02:32
So you can use the bank, but you should be able to solve these without the bank if needed.
02:40
So let's go ahead and go through the answer to each one.
02:45
So one states no one is perfect.
02:50
So this is going to be, remember this is the for all x not two is not everyone is perfect.
03:05
So this is the not symbol again for all x p of x.
03:13
Now it says all your friends are perfect.
03:18
So we're going to go ahead and introduce the f of x now.
03:21
So for all x f of x p of x...