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Current time:0:00Total duration:10:36

- [Instructor] Now we're going
to work through the questions for our grouping setup. Make sure that you
watched the video in which I walked through the initial
setup and deductions, before you continue with this video. And at any time, feel
free to pause the video, if you wanna try a question
before I explain it. This first question is
an orientation question, and you usually get
one of these per setup. It reads, the student could
take which one of the following groups of courses during
the summer school session? In other words, we're asked to determine which choice is an acceptable list of courses that the student takes. That means that four of the
choices, the wrong ones, will break at least one of the rules, and the answer won't
break any of the rules. The great thing about these questions, is that you usually
don't need any deductions to get a quick and accurate answer. We'll show you an
approach that you can use in order to save as much time as possible. It's usually a good idea
to start with the rules, instead of the choices. If we look at each rule and eliminate the choices that violate that rule, then no matter what the
answer ends up being, we will have gone through
all of the rules only once. Let's see how to do that. Our first rule tells us
that if history is in, then statistics and music
can't be with history. If we look at the choices,
which ones can we eliminate? Well a is out, because
history and statistics are both listed in a. We can also eliminate b,
since history and music are both listed in b. We never have to consider
those two choices again, and we've only gone through one rule. The second rule is that if music is in, then physics and theater are both out. Looks like we can eliminate e, which shows music and theater both being in. And the last rule is
that if writing is in, then physics and statistics are out. Here, we can cross off d,
because we see in that choice that writing and physics are both in. That means that c is the
only choice that's left, so it is our answer. To summarize what we just did for this orientation question,
we started with the rules, and eliminated choices
that violate each rule. If we had started with the choices, we would've had to go through each rule three times, in order
to get to the answer. Instead, by starting with the rules, we only had to go through the rules once. The wonderful thing about
this kind of question, is that they're very common, and they're a good one to
get out of the way first, since they usually don't require
any deductions or drawing. Here's a maximum question. We're asked to figure out what's the highest number of
courses the student can take, without breaking any rules. These can often be pretty challenging, but let's work through this
question one piece at a time. We know from the introduction
that the student has to take at least three courses, and
now we have to figure out what the highest number of
possible courses could be. It's really good that we thought
about eliminating elements when we were making deductions. Because, if you remember
which course we said had the highest impact, it was music. We recognize that if music is chosen, then a whole bunch of
courses can't be chosen. So since our goal is to
maximize the courses, we wanna make sure not to select music. So let's put music in the out column. And that takes care of choice a. Let's think about the opposite extreme. Which course can we certainly choose without worrying that it
will affect our maximum? Linguistics, so let's
place linguistics in, since linguistics doesn't
have any relationship with any of the courses, so we can safely choose
it any time we want. Okay, which of the remaining five courses is almost as free as linguistics? In other words, which course
only affects one other course? That would be theater, so
if we're wanting to maximize our number of courses, theater
is going to be a safer bet than the other classes that
knock out two courses each. Okay, let's be strategic here. We're always taking
inventory of who's left, who's unaccounted for, right? And it looks like history,
statistics, writing and physics, are unaccounted for, as of this moment. Well we definitely can't take all of them, because every single one of these courses knocks at least one other course out. But notice that these remaining elements, are all involved in rules together. We can pair them this way. We can say either history
or statistics is in, since they can't both be in, and then either writing or physics is in, since those two can't both be in. There's no way that we can
get more than two courses out of this list before,
so we have our answer. The maximum number of courses the student can take is four, answer d. To recap, you will always
have enough information in the rules, and in the
questions to find your answer. Many times you'll have
to be strategic though. In this case, we used our
knowledge of eliminating elements, and freer elements, in
order to find our maximum. If the student takes
neither physics nor writing, then it could be true that the student also takes neither x, nor y. We're given a new
condition to consider here. So, with a new and temporary
condition to consider, let's re-draw our initial diagram, and establish that physics
and writing are both out. It's common for students
to feel stuck at this point in the question, because
we don't know what happens when physics is out,
or when writing is out. We only have rules that
tell us what happens when the class is in. So we have to look beyond the rules, and once again consider
the impact of the numbers. If physics and writing are both out, and each of the choices
lists two more classes that the student wouldn't take, that would mean that four classes are out, and three are in, in this scenario. So that helps a ton. We can test each choice
pretty quickly by writing down which courses are the
ones that are selected. Then, because we're looking
for a could be true, we'll expect that four of the
choices will break the rules, and one of them will not. In choice a, the courses that are out are history, linguistics,
physics and writing. And that means that music,
statistics, and theater would be the courses that are in. Well that doesn't work,
because music and theater cannot be taken together,
according to rule number two. Let's eliminate this and move on. Choice b, the student would not be taking history, music, physics, and writing. So that leaves linguistics, statistics, and theater to be in. This works, so we can
stop here on testing, select the answer, and move on. To go through the remaining
wrong choices quickly, choice c leaves us with
linguistics, music, and theater, and that breaks a rule
because music and theater can't be together. Choice d leaves us with history,
statistics, and theater, and that doesn't work because
rule number one tells us that history and statistics
can't be together. And choice e leaves us
with history, linguistics, and music, and that doesn't work, because rule one again, tells
us that history and music can't be together. B is the answer here, and to summarize, we couldn't have gotten
this point so easily without staying vigilant
about the number limitations. The answer was not obvious
from the list of rules alone. Instead, the answer came from the numbers, as well as the rules. In this question, we're given
new information to consider, because the question asks,
if the student takes music, then which one of the following
must the student also take? Because we have a new condition, we'll re-draw our initial diagram, and establish the
condition by putting music in the in column. Now it's time to make deductions. We know from the rules that
we have a lot of courses that can't be taken alongside music. And those courses are
history, physics, and theater. Well, we've figured out three
courses that can't be chosen, but what about the
courses that are chosen? We're gonna have to dig a little
deeper for more deductions, and to do that, let's remember to consider the numbers of the situation. So far, we've established
four courses concretely. There are seven total courses, and we know that at
least two of those seven need to be chosen in order to meet the minimum of three courses. Let's list the courses that
aren't accounted for yet. We haven't yet placed linguistics,
statistics, or writing. Excellent, do we know anything about these courses based on the rules? Well, linguistics isn't in any of the rules, we know that. Statistics, we know, can't be selected alongside history, or writing, aha! Statistics and writing
can't both be selected because of the last rule. That means that linguistics
is definitely in, and then the third course selected is either statistics or writing. And then the other, of
statistics and writing, is out. So the question asks us, which course the student must also take. The answer is e, the student
must take linguistics. All of the other choices list courses that either must be out, or could be out.