MOck_test_Q12 appears to have wrong answers...

[Anand Iyer]

S2 is {1,9,265} with a cardinality 3

Unless you include 1 twice, it'll not have a cardinality 4, as indicated.  As far I know, we can't include any item twice in a set.  I remember this mentioned in one of the lectures too.

Thus, the 3rd option also can't be right.

Team, can you comment.

[Dhannya POD]

Set S2 contains elements corresponding to n, not f(n).

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Dhannya. S. M,

IITM Online Degree Project,

IIT Madras.

[Anand Iyer]

oh, what a joke!!!

sorry, couldn't hold myself...I never expected this answer.

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Cheers,

Anand

[Sherlock Holmes]

But when we are including a value in a set, we do eliminate duplicates. As per the definition of a set , it cannot have duplicate elements so how can cardinality of a set consider the contrary?

[CG]

I got it wrong too because I made a calculation mistake for n=4 while hurrying to finish. 

On Wednesday, November 11, 2020 at 9:34:10 PM UTC+5:30 anandd...@gmail.com wrote:

[Anand Iyer]

Detective, 

that's the issue here.  What Dhannya clarified here is that we need to include n-values (1,2.3...) and not f(n).  and, n-values will not anyway have duplicate values, because they're natural numbers <=6.

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Cheers,

Anand

[Priyanshu Singh]

so s2 has caridnality 3 then why is 4 correct, and how t is just 2  as question says n is greater than equal to 2 so it can go till infinity as it has no limit for n unlike s1 and s2 then why isnt cardinality of t infitinty?

[Anand Iyer]

Cherian,

nice to see the table nicely laid out.

I don't know if you noticed it, identifying the set T is not straight-forward. two things here.

1.  It's not {2}, it's {3}.  We've to include n not f(n)

2.  This point is more important.  elements in T don't have the condition that n has to be less than 6.  Looking at just that aspect, T can have infinite items.  How is the cardinality of T, 1?  Hope you figured out...

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Cheers,

Anand

[Anand Iyer]

So Priyanshu,

the point is we've to include all n-values that has odd values for f(n).  there're 4 such n-values.

On the second question, you're right.  T could have infinite points, unless we don't consider that every calculation of f(n) has two factors.  So, every T has a factor.  So, there's no other element than {3} in T.

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Cheers,

Anand

[Aswathi Mohan]

T by definition contains only those numbers whose function value is prime (therefore it cannot be written in terms of product of numbers other than 1 and itself). If we look at how f(n) is defined, clearly it is a product of 2 numbers n-1 and f(n-1)+f(n-2). so f(n) becomes prime only when exactly one (and not both) of n-1 or [ f(n-1)+f(n-2)] becomes 1, which happens only when n=3  

[CG]

1. Yes it should be 3. Hunger is kicking in . Careless mistake.

2. Cardinality is 1 because the function generates based on multiplying by (n-1) : So for all numbers above 6, (n-1) will also be a factor.

[Sherlock Holmes]

Thank you for the clarification Anand.I have once again made the error of not reading the question properly.

[Malabika Guha Mustafi]

Ok got it. We need to consider n when f(n) is prime. hmm

[Malabika Guha Mustafi]

@ Aswat, nice explanation.

[viju...@gmail.com]

In my view, S2 should be {0,2,4,6} with Cardinality = 4. Because at

f(0) = 1,

f(2) = 1

f(4) = 9

f(6) = 265

All the output of f(n) are ODD and n <= 6, thus satisfy the criteria for S2.

Dont shoot me if its not correct :).

Regards,

Vijender

[Anand Iyer]

you'e correct, Viju.  I'll not shoot.  Relax...

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Cheers,

Anand

[Mathematics 1 Support 2]

Hi Anand,

You have been a good responder to the question being asked in the discussion forum. 

Hi all,

The team always tries to respond to all of the questions asked by students. Sometimes we do not get the question and sometimes students are not clear with their questions, so mistakes happen. It would be great if we support each other.

By the way nice table.

Best wishes,

Rahul

[death god# Reaper]

I have a silly doubt. Is 0 even number.
 What about -2

[death god# Reaper]

I have a silly doubt. Is 0 even number.
 What about -2

On Thursday, November 12, 2020 at 10:05:19 AM UTC+5:30 maths1-...@onlinedegree.iitm.ac.in wrote:

[Thokchom Phalguni Singh]

yes both are even numbers.

[Sree Kavitha]

if u any notes pl share with us for maths

imstudying after 10+yrs gap. couldn find proper notes . 

pl help