Grouping setup | Video lesson

let's take a look at that group being set up together and to do so we'll start by examining the introductory passage to understand what we're being asked to do the passage reads a student is choosing courses to take during a summer school session each summer school student must take at least three courses from among the following seven history linguistics music physics statistics theatre and writing the summer school schedule it restricts the courses a student can take in the following ways all right so the first thing we can notice is that the primary players are seven summer school courses we can make a list of them here so that we can keep track of them we've got history linguistics music physics statistics theatre and writing now what are we doing with these courses we are choosing courses to take and we're told that we have to choose at least three of the seven we're not seeing any kind of ordering component happening in the set up so that means that this is a classic grouping setup let's make a diagram that has a column for the courses that are chosen which we'll label as in and a column for the courses that aren't chosen which we'll label as out so if we weren't given any minimum numbers to work with we would be finished with the basic diagram but because we're told that there will be at least three courses chosen then we can reserve three spots in the in column for those courses that are chosen and there could certainly be more than three but we won't draw spots unless we know for sure that something will occupy that spot at this point we have a basic diagram and we can move on to the rules looking at our rules we can see that we're working with three conditional rules the first one tells us that if history is in then statistics is out and music is out we can map it using arrows if we wanted to and write that if history is in then stats is out and music is out the logically equivalent rule is that if statistics or music is in then history is out however we could make it even easier for ourselves this rule is really telling us that history and statistics will never both be in because it can't happen according to this rule if history is in then the statistics is out and if statistics is in then history is out they can't both be in likewise we know that history and music will never both be in for the same reason so instead of writing it all out the way we did we could use a shorthand notation to represent it there are lots of ways that you can notate the fact that two elements can't be together when we like the box with a line through it it's just one short and simple way to do it and it keeps our notes really nice and simple we see the same pattern in the next rule if music is in then physics is out and if music is in then theatre is out so we can make more deductions music and physics can't both be in and music and theater can't both be in luckily for us the exact same pattern expresses itself in the last rule if writing is in then physics is out and if writing is in then statistics is out at this point we're done with the rules and it might seem like we could just move right on to the questions we've got a bunch of conditional rules and we could be tempted to think well it's all if rules so there's really nothing concrete to see here sometimes though that's not actually quite true given that we have six pairs of elements who can't be together it's worth thinking about which elements are the most restricted and which elements are the least restricted let me show you what I mean take a look at the list of courses and see if you can tell which course is the least restricted in other words which course is completely unaffected by the other courses and if you thought linguistics then you are correct since linguistics isn't in any of the rules then it's completely free to be selected or not selected in any given situation what about the opposite end of the spectrum if you look at the rules we wrote down which element seems to be the most limiting in other words which element is involved in the highest number of rules it's music take a look music is involved in three of the roles and no other class is involved in that many to put it into everyday context imagine that this were a set of about people being invited to a party and if music goes to that party three people have to go home that's a really big impact that music has if linguistics goes to the party nobody has to go home so as you move through the questions it will be helpful to keep both linguistics and music in mind as the least and most limiting elements to recap we just set up a grouping task using the in and out diagram and instead of writing out all of the conditional rules in full we notice that these particular conditional rules had a pattern that we could take advantage of in our notation we created six pairs that we know can't be selected together and from that we recognized linguistics as our least limiting class and music as our most limiting class we are in a really great position to move to the questions because we have an initial diagram that we'll use for support as well as a solid understanding of the rules