For each of the following premises, what relevant conclusion...

For each of the following premises, what relevant conclusion can be drawn? Use the rules of inference to obtain the conclusion from the premises. "If I work, it is either sunny or partly sunny." "I worked last Monday or I worked last Friday." "It was not sunny on Tuesday." "It was not partly sunny on Friday" Let: p ="If I work, it is either sunny or partly sunny." q ="I worked last Monday or I worked last Friday." r = "It was not sunny on Tuesday." s= "It was not partly sunny on Friday"

Transcript

00:01 Okay, for this question, they give us several different statements, and they want us to find the conclusion that we can draw from those statements using the rules of inference.

00:11 I'm going to set up a little chart right now because we have a lot going on in this question.

00:17 We have three days of the week.

00:20 We have monday, we have tuesday, and we have friday.

00:25 And then we have a couple of different qualities here.

00:30 Did we work? yes, no, or maybe.

00:35 And what was the weather? and based on this kind of chart that we can start to fill in here, hopefully this can start to lead us to the conclusion that we can figure out.

00:52 So i'm going to write all of our given information in blue so that we can kind of follow what happens here.

00:59 So let's start with just the definitive statements.

01:02 So not looking at any of the if -thens, but just the definitive statements.

01:08 So the first one says, i worked last monday or i worked last friday.

01:15 So did we work? maybe for monday and maybe for friday.

01:24 We maybe worked on monday or we maybe worked on friday, one or the other or both.

01:31 Other information that we're told was it was not sunny on tuesday.

01:36 So the weather on tuesday, not sunny.

01:39 We are given that information.

01:45 We're also told it was not partly sunny on friday.

01:57 Okay.

01:58 So now that we have all of this information, let's see if there's anything that we can figure out.

02:04 Of course, we also have the conditional statement.

02:07 If i work, it is either sunny or partly sunny.

02:12 So we can kind of look at some of our information here, where if we worked on friday, let's say, then it has to be either sunny or partly sunny.

02:28 So then it would have to be sunny because it's not partly sunny.

02:33 But that's not really a conclusion because that hinges on if we were to work on friday, which we're not sure if we did or not, because we either worked on friday or on monday.

02:46 So even though this is something that you could figure out, this doesn't really count as our conclusion yet...

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