## PrepTest 78, Game 1, Setup

### Transcript

This is PrepTest 78, Game number 1, and in this game we are dividing these seven workers into two different groups. One group is the group that's selected to the project and the other group is everyone who is left off the project. So you can think of this an in an out grouping game, there's an in-group, the group that's selected and an out-group, the group that's not selected.

And it is a fixed grouping game because we know exactly how many are gonna be in, three are in and four are going to be out because there's a total of seven, so that's why I'm going to draw our fixed grouping setup with three in and four out. I'm also going to list my seven variables up near the main diagram. Now you should also notice that we are told that exactly one of the in-group members, the project members.

Will be a project leader and one way to handle that is just to draw a PL next to the in group like this. That way it's unreminded that one of this in-group members will have to be PL project leader, I don't know exactly which slot I want to assign that to just yet, so that's why I'm leaving it off to the side. Now let's move on to the rules, and the first rule says that Q or R can be a project member, only if leading the project, the phrase only if here is our conditional indicator.

And remember from our conditional logic lessons that only if Is introducing a necessary condition, it's introducing the then side of a conditional statement. So one way to think about what this rule means is, if Q or R is a project member, then, and here's our conditional arrow, then they must be leading the project. If you put a Q in the In-group like this, then the project leader has to be Q. If you put R in the group like this, then the project leader has to be R, so I'm going to diagram that in my list of rules like this, where if Q is in then Q must be project leader, if R is in then R must be project leader.

Notice that I've also diagrammed the contrapositive of these rules and the contrapositive is what we get when we switch both sides of the arrow and the gate. So that means if Q is not project leader then Q is not in and if R is not project leader than R is not in. You might notice at this point, that this means Q and R can't be in together at the same time because if you tried to put Q and R both in together at the same time, well now only one of them gets to be project leader, but rule one is saying both of them have to be project leader.

So that's why this right here is not possible at least one of Q or R Is gonna have to go out at all times. Now let's take a look at the second rule, if Smith is a project member, then Taylor also must be. So here we have a R if, and that is the sufficient side of our conditional statement.

If Smith is a project member, then the arrow goes to the right, Taylor must also be a project member. I'm gonna diagram that like this, if S in then T is in, the contrapositive means if T is out then S is out. The final rule, says if Wells is a project member, neither R nor V can be a project member.

So again, we have the If, which introduces the sufficient condition, the, If side of our conditional, if you put Wells in, then that means you can't have R and you can't have V. On the diagram the third rule like this, if W is in then that means R out and V's out the contrapositive you'll notice, when you have a contract positive of a statement that has and on one side of the arrow.

What you have to do is you have to switch both sides of the arrow and negate all the terms but change the end into an OR, so that's why it becomes if R is in OR, you put V in, then that means W is out. So now that we've diagrammed our rules, I wanna make sure that we go ahead and circle our floating variable, here the X which is not mentioned in any of the rules, so X is the least constraint.

And I also wanna give some thought to whether there are any deductions that we can make based on our rules. Now unfortunately, there aren't any connections that we can make between these rules. You can see that R is mentioned in both rules one and rule three, and so we do know that if R is in, R is gonna be the project leader, and if R is in, that means W is out, but there really isn't any other connection to be made between these rules beyond that idea.

So that means that this game is likely to won where we just have to do work on the questions, and be ready to sketch out a diagram for each question as necessary.

Read full transcriptAnd it is a fixed grouping game because we know exactly how many are gonna be in, three are in and four are going to be out because there's a total of seven, so that's why I'm going to draw our fixed grouping setup with three in and four out. I'm also going to list my seven variables up near the main diagram. Now you should also notice that we are told that exactly one of the in-group members, the project members.

Will be a project leader and one way to handle that is just to draw a PL next to the in group like this. That way it's unreminded that one of this in-group members will have to be PL project leader, I don't know exactly which slot I want to assign that to just yet, so that's why I'm leaving it off to the side. Now let's move on to the rules, and the first rule says that Q or R can be a project member, only if leading the project, the phrase only if here is our conditional indicator.

And remember from our conditional logic lessons that only if Is introducing a necessary condition, it's introducing the then side of a conditional statement. So one way to think about what this rule means is, if Q or R is a project member, then, and here's our conditional arrow, then they must be leading the project. If you put a Q in the In-group like this, then the project leader has to be Q. If you put R in the group like this, then the project leader has to be R, so I'm going to diagram that in my list of rules like this, where if Q is in then Q must be project leader, if R is in then R must be project leader.

Notice that I've also diagrammed the contrapositive of these rules and the contrapositive is what we get when we switch both sides of the arrow and the gate. So that means if Q is not project leader then Q is not in and if R is not project leader than R is not in. You might notice at this point, that this means Q and R can't be in together at the same time because if you tried to put Q and R both in together at the same time, well now only one of them gets to be project leader, but rule one is saying both of them have to be project leader.

So that's why this right here is not possible at least one of Q or R Is gonna have to go out at all times. Now let's take a look at the second rule, if Smith is a project member, then Taylor also must be. So here we have a R if, and that is the sufficient side of our conditional statement.

If Smith is a project member, then the arrow goes to the right, Taylor must also be a project member. I'm gonna diagram that like this, if S in then T is in, the contrapositive means if T is out then S is out. The final rule, says if Wells is a project member, neither R nor V can be a project member.

So again, we have the If, which introduces the sufficient condition, the, If side of our conditional, if you put Wells in, then that means you can't have R and you can't have V. On the diagram the third rule like this, if W is in then that means R out and V's out the contrapositive you'll notice, when you have a contract positive of a statement that has and on one side of the arrow.

What you have to do is you have to switch both sides of the arrow and negate all the terms but change the end into an OR, so that's why it becomes if R is in OR, you put V in, then that means W is out. So now that we've diagrammed our rules, I wanna make sure that we go ahead and circle our floating variable, here the X which is not mentioned in any of the rules, so X is the least constraint.

And I also wanna give some thought to whether there are any deductions that we can make based on our rules. Now unfortunately, there aren't any connections that we can make between these rules. You can see that R is mentioned in both rules one and rule three, and so we do know that if R is in, R is gonna be the project leader, and if R is in, that means W is out, but there really isn't any other connection to be made between these rules beyond that idea.

So that means that this game is likely to won where we just have to do work on the questions, and be ready to sketch out a diagram for each question as necessary.