darn wrote:
bethebest wrote:
Bunuel Can you please explain why we are considering an OR scenario. We should find out the no. of cases where A and B are together as well as D and E are together.
Hence AB C DE = 3! *2*2 = 24
This should now be subtracted from 120 and the answer should be 96.
Can you please explain what am i missing here?
Thanks.!
I have the exact same question.
Can
Bunuel/
VeritasPrepKarishma/
mikemcgarry /
Abhishek009 / b]chetan2u[/b] or any other expert please confirm why we are using the Or condition when the question clearly states:
How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B
and D is not adjacent to E?
If the question was :
How many different arrangements of A, B, C, D, and E are possible where neither is A adjacent to B nor is D adjacent to E, then the OA does make sense.
Could you please confirm if my understanding is right?
A reply will be much appreciated.
Dear
darn,
I'm happy to respond.
My friend, I don't know how much formal logic you have studied. Students sometimes naively treat the word "
not" as the equivalent of a negative sign and treat the word "
and" as the equivalent of multiplication, and then try to apply the Distributive Law. The problem, though, is that the word "
not" does not distribute they way that numbers would.
(not A) and (not B) \(\neq\) not (A and B)Let's think about a real world example. Let's say I have a company and I am hiring. Let's say A = no college education, so I can't hire somebody with condition A. Let's say B = constantly covered in insects, so I can't hire somebody with B (it's unclear whether this would be construed as discrimination under current labor laws).
Suppose I post a sign #1:
We hire only people who are not A and not B.
Person #1 has no college education but no insects (A and not B)
Person #2 has a college education but is constantly covered in insect (B and not A)
Person #3 has no college education and is constantly covered in insect (not A and not B)
All three people are automatically excluded by that sign, because that sign specifies two conditions that must be met simultaneous--the "not A" condition and the "not B" condition. We ask each person two questions: are you A? are you B? Both have to be "no" answers to be included. Each of these three people would say "yes" to at least one of the questions, so all three would be excluded.
Instead, suppose I post a sign #2:
We hire only people who are not A and B.
Here, we are excluding simply one condition, the condition of having both A & B simultaneously. We ask each person just one question: are you both A and B at the same time? Persons #1 and #2 can truthfully say no, because each of them has only one of the conditions, and only person #3 has to say yes. Thus, this sign still excludes poor person #3, but now person #1 and person #2 would be included, because neither one of them has the combined condition of A & B simultaneously. This has a different effect than sign #1 had!
In fact, and this is the part that can be really confusing for people who haven't studied formal logic,
(not A) and (not B) = not (A or B) Similarly,
(not A) or (not B) = not (A and B) Think about a third possible sign, sign #3, saying:
We hire only people who are not A or B.
Here, again, we are excluding just one condition, but now it's the condition of A or B. Again, we ask each person just one question: are you either A or B? All three people would have to respond yes to this question, so all three would be excluded.
The same people are excluded by sign #1 and sign #3, so those two signs have the same meaning, but sign #2 has a different meaning.
The folks who solved this math problem correctly used these logical principles correctly.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)