Excellent material on set , relation and function..shared by Srijnava

[Malabika Guha Mustafi]

[Anand Iyer]

That's nice.  Thanks for sharing, Malabika.  

On Saturday, November 14, 2020 at 2:48:23 PM UTC+5:30 Malabika Guha Mustafi wrote:

[D Vidya]

Thanks Malabika.

On Saturday, 14 November, 2020 at 2:48:23 pm UTC+5:30 Malabika Guha Mustafi wrote:

[nikhil kambli]

i get confused 

how much ever i try for reflexive relation

symmetric and trasnative is good

antisymetric is also confusing

[satyasanthi ponnala]

thank you

On Saturday, November 14, 2020 at 2:48:23 PM UTC+5:30 Malabika Guha Mustafi wrote:

[Malabika Guha Mustafi]

@ Nikhil , Really?

 Actually transitive concepts is little bit confuising.
Reflexive is the easiest.

Only one thing you should remember, all the diagonal pairs should be present in set.All should be present. If you share your confusion, we may try to clear it out.

For all a= co responding b if satisfies then it is reflexive.

[Ganesh K Pillai]

Thanks for the material Malabika !!!!

I have a query on Reflexive with regards to the example given  mod of a-b <= b ...

https://groups.google.com/a/nptel.iitm.ac.in/g/ma1001-discuss/c/Ss17tRyP5pw/m/7bHsR9BMBQAJ

Thanks 

[Malabika Guha Mustafi]

We should give thanks to @ Srijnava who shared the materials. I just repost it to reach maximum people.

[Maria Joseph]

Cn any one explain the powerset of {{1}}.Will the cardinality of powerset of this set be 2 or is it 4?

Pls reply...

Regards

Maria

On Saturday, 14 November 2020 at 14:48:23 UTC+5:30 Malabika Guha Mustafi wrote:

[Ayush Bharti]

Can any one reshare the material I m not able to find it.

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[Sofia Sagar]

  hello nikhil bro ,

we meet again (pure coincidence . lol )

anyhow i thought i could clear off your doubts

reflexive relation means : there may be any type of pairs : (a,b), (b,d),(c,e)......anything but..for every first element you should have an identity pair too i.e. 

                                                                                                     if we consider these three above pairs ...for the set to be reflexive we must also have elements (a,a).                                                                                                       (b,b), (c,c). we dont need to have (d,d) since it is a second element . like wise (e,e) need not be ! 

antisymmetric : this is opposite of symmetric relation

                              i.e. if we have (a,b) in the set then compulsarily (b,a) should not be ! 

hope this helps :)

[Ganesh K Pillai]

My understanding  

It’s a powerset with 2 subsets 

1. The empty set 

2. The set which has element 1.

So cardinality of the said powerset is 2.

Thanks 

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[Malabika Guha Mustafi]

@ Sofia for antisymmetry, ( b,a) should not be there but except when b=a it should be there.( like a is subset of b. when both are equal then b is also subset of a but hen a is not equal to b then b is not subset of a hence anti symmetry).

for asymmetry ,b=a should not be there.

so, for antisymmetry, one set can be reflexive but for asymmetric , the set can not be reflexive.

[nikhil kambli]

Thanks a lot for sharing. 

[Sofia Sagar]

thank you 

[Sofia Sagar]

hey  guys ,

was reading the material and in pg 14( i guess .... somewhere around there) it states Q,R,Z are all infinite

so just reminding you guys that Q,Z are countable 

but R is not countable ( not there for qualifiers )

guess you all know ( was mentioned in maths class week 1 ) but still reminding 

and @  Malabika Guha Mustafi  thank you so much for pointing out that about assymetric and antisymmetric functions . that really helped me (i never knew!):)

[Malabika Guha Mustafi]

@ Sofia, That's little bit advanced topic . Better think that all are infinite.

[Kanaghadhara N E]

please explain sse

On Saturday, 14 November 2020 at 14:48:23 UTC+5:30 Malabika Guha Mustafi wrote:

[Malabika Guha Mustafi]

What is the main reason to compute SSE

Y= mx +c ( y is a function of x and some constant)

According to theory , all y should obey the function formula so if we plot all y  then we will get a straight line . But in practical, we always get Y which are slightly deviated from what their values are supposed to be. So if we plot then instead of getting all values of  y on a straight line we are getting scattered y points nearby a straight line but not exact on straight line. so our goal is how can we fit the all y near to a straight line means  how we can minimize the  difference between actual y value( after observation)  and corresponding  y value of the fitted straight line.

That is the main reason to find out SSE which is minimum .( considering different m value of an equation).

How to compute SSE:

1. First check which is function of other.( which is y)

It will definitely mentioned in question. For example, P(T) was mentioned in graded question. so P is function of T. It means P=y and T=x

2. If the table  ( different x,y - observations value)is given, that means m is already given in equation.

Y=mx+c. [c may be constant or 0].

example:

1. Activity 3.5

If a line fit y=x+1 is given for the data as shown in Table AQ-3.1, then compute the Sum Squares Error (SSE).

Here, m=1, c=1

2.  Graded assignment

Determine the gas constant R, two students A and B perform an experiment based on the ideal gas equation given as Pv=RT . Both use the 

   same gaseous sample having v=16.6m3/mol and reported the approximate value of R as 8.3J/(KΔmol) using the minimisation of sum squared 
   error. The data collected by both the students are reported below. Choose the correct option:

Here,

Pv=RT

so, P= R/v T

m=R/v  and c=0

No matter, in which form you are getting.

 it is representing y=mx +c

3. Then put the formula SSE= sum of ( yi- mxi-c)^2.

Hope it is clear now.

[Malabika Guha Mustafi]

If the relation between x and y is as shown in Table AQ-3.2, then which among the following lines is the best fit? ( Week 3..Activity 3.5)

Then, for each m( the answer options we need to compute).

 It is time consuming but straight type of question.

[Janani Suganya]

Thank you Malabika