Equivalence Class - Relations & Functions Video Lecture - Class 12

hello friends this video on relations
and functions part 10 is brought you by
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before watching this video please make
sure that you have watched part 1 to
part 9 clear our concept of equivalence
class the new term please pay a little
at the Asian here so let's say there you
are the equal relation on sin T then it
decompose a into pair wise disjoint
subsets
he is known disjoint subsets and all the
imagined subsets are related to one
another under the relation and no
elements of subset is related to any
other what I mean to say is if you have
a set a itself which has some anyway and
let's suppose a but despite a cross a a
light across a here what will give even
even with one set even will eat your
normally even if it will be one living
guard are not even yeah right and then
you would start with E you're done with
this then you started a to do even then
a we do not really in your name and then
you started let's suppose en anyone not
but I'm in this already the element of a
cross B now I do every relation is
nothing but a subset a subset of this a
cross key now now what I'm trying to say
is equivalence class the concept is the
first thing for you get it means class
the first thing is the relation has to
be when I say equals relation
it has to be transitive symmetric
reflexive so if it is reflexive
transitive insipid
equivalence relation in the illustration
Ashley it decompose these values into n
number of subsets example this R
whatever you can decompose into n number
of subsets if it is read equivalence
relation and it decomposed in such a
fashion that all the subsets which again
are disjoint sets that means if this is
part of set one this won't be part of a
Mississippi so this is what this this
elements of are no set wrong this so
this is one we borrow segment and the
other elements this is part of set - so
these be part of sector they are
disjoint example this element can be
part of my level sets subsets certainly
madam only one Sampson and that is hot
decomposing for example I think for
example of a height when I say height of
person is equal to five percent this
kind of relationship we have seen was an
equivalence relation correct because
this is reflexive height of p1 is equal
to had to be a symmetric also going to
be to keep this will appear and quantity
also because if he was going to be 20
this will be P 3 P 1 is equal to V so we
have seen this that height of person if
you compare each all relation this is
equal efficient now if you see this this
is bunch of people living in a family
like this is multiple family and now on
this I am
we know that this is the equivalence
relation first thing is EQ relation yes
first step plus it is X relation
second thing is it will decompose into
player wise distances you see this
hideout this guy won't be pretentious
name but height of these three
fight on these three are equal and I got
these three now you see this is nothing
but by second one this is working
goodbye set 2 and this is nani mo Peng
City
now what I observe here is all this sets
are exclusive and they're disjoint that
is the end of this guy is not power to
sit it's part of only one set any guy to
make this little game is part of will
essentially they are only part of one
set they are disjointed and the
equivalence relation holds true for all
this example from Bhagavad set one
equivalence relation holds true talking
about this set the accumulation relation
world's tools I'm talking about this set
in this set also the equivalence
relation forced this is how example of
equivalence class looks like this is a
real line example they give you some
mathematical example in the next place
but this is how equivalent classes first
thing equivalence relationship going to
and then we divide those into pair of
disjoint subsets you see this joint
subside 1 and so an entry or a disjoint
is there is no common element and if you
combined all this you get the whole is
correct combine all this rhythm element
so the rule even to combine and the
equivalence relation holds true for this
set this set and you see this set the
heights are equal this guy is equal to
this this guy that is reflexive this
guy's you can take this guy
this lady and this name is this the type
that is symmetric and height of 1 is
equal to height of 2 by 2 is equal to
height of 3 this implies kind of man is
kind of a two three a test done
similarly in this case also if you see
ba and leading the a B and C a is equal
to B right he is going to writing
because my
reflexive is going to be
he is going to a that is symmetric is
going to be he is good to see right that
nice high top a is where to hi W it is
height of a square to a height of see
that implies transitive
so if you see all this G our equivalence
relation so I am saying is equivalence
class or nothing but all this sets set
one is equivalence class said to his
ignorance class and said Lisa
equivalence all right so what I've got
is the whole thing is not a dissipated
into set 1 plus Z 2 plus safely and all
these sets are disjoint sense and this
is nothing but would be P is nothing but
my set the complete set complete set all
family members
o handle one family business so those
guys are cut off said a and this set is
broken you said one set to say 3 now
this n summation explicit and all of the
sets are holding equivalence relation to
having a go stupid real example of
cheapness graphs let's take a
mathematical example of equivalence
class let n be the set of all natural
numbers correct any set of all natural
number 1 2 3 4 5 6 is nothing but my end
the national airline and mmm are members
of this set now we defined an
equivalence relation between N and M
that is mmm lives same we went 11/5 this
is a equivalence relation has to you
take any element and we divide by 5 it
should give same remainder that is a
relation equal relation actually if you
see same remainder when divided by v
naught we observe we can divide this
decompose this into even a 23 deepening
why if you divide 1 by 5 polishing and 1
so I'll say this first right like this
just to leave you one if you divide two
by by budding it to the vendor 3 by 5 8
3 4 by 5 you get 4 5 by 5 we get 0 6 by
5 again you get 1 let's go to 7 here
save a 5 you get to 8/5 get 3 my left
anything so take my 5 in 5 you see
drippage like this one to this so what
do you do we can bucket this into
buckets where you see even is nothing
but all the number which leaves
remainder is 0 1 2 is in effect that
this I am doing 5 10 15 20 is kind of
numbers
all right into is nothing but numbers
which leads defender 1 divided by 5 that
is 1 6 and then we have 11 these kind of
numbers are thick which leaves one when
divided by 5 again a three jeeps - so I
have two and I have seven then actual 17
then I have a four which leaves three
when divided by 5 so I have 3 the land
age 18 all these number takes 3 bind a
vector fine then I have if 5 sleaze for
20 wiper friend so I have four this
gives four in here 5 9 is 14 then a 90
mother
so these if you see it has all the
numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 any night there's all the numbers
plus they are all mutually exclusive
giant sets there is no element which is
forward to book them or any cassettes if
one is here it will not be in Universal
two is here do not be innocent
so what we have seen that the bigger set
we want to infinity is divided into five
subsets fight this joint subsets correct
and if you see there is no common player
if you take on disorient of even in also
any sense
take these two even it'll you try to
find even in the dictionary do you get
fight I think because there is no common
element
similarly if you take a MLA three also
you will get nothing they gave and you
they gives you don't think you need any
two combination and you will see that
there is no power limit
also if you see that these subsets hole
equivalence relation thank you visit
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