Roster & Set Builder Form (Part - 2) - Sets, Math, Class 11 Video Lecture

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methods of the representing acid they
are 2 methods to represent I said what
is the roaster form and the second is
set-builder form we discuss both of
these norm roaster form in those two
form all the elements of the set are
listed and they are separated by comma
and enclosed with braces
please no they are three things that is
important all the elements are listed
they are separated by comma and they are
enclosed with laces for example when we
say give me the set of all numbers here
in dice
so we in all know that these numbers are
the only numbers will appear in die in
die you can have 1 2 3 4 5 6 so when you
see that I want to represent using
roaster form what we do is we write all
the elements so all the elements are 1 2
3 4 5 6 and now we do a comma situation
comma comma comma comma comma and
enclose in the braces that's what we do
and we do this this is called roaster
form for example when we say set up all
bobbles you will see something this e e
I so you see what I have done here is I
have written down all the elements
separated by comma enclosed in the
braces this is the representation of
roster form now there are some points
that we should note in those two form
first the order of the element is
immaterial for example in the same
scenario if you see e e I owe you
setup all bubbles or we see a you I owe
you I going
all we see you II I way or Bowie I mean
you all are same as long as the number
of elements and the elements are see for
example all these cells contains a I yo
you the order does not matter
so please note the order is immaterial
or it does not matter in roster form
similarly the dots at the end tell us
that the set is infinite tell us that is
wrong here we can be convinced that that
set continues infinitely for example
when we say the set of odd national
numbers we say 1 3 5 dot dot dot that
means this say continuous infinite this
is this is as good as one three five
seven nine eleven thirteen fifty you
keep on going so this is what how we
represent infinite set you put three
dots in the end
similarly in those two form generally
the element is not repeated the element
is not repeated please note it is not
repeated for example when we say we want
to form a set of the letters forming
school so we see here SC H Oh L these
are the only four or five distinct
letters O is twice so when I say the set
of letters forming school
I am included or only once I have not
included one wise o is included only
once so that means in rows to form the
element is generally not fitted let me
reiterate again because the solution in
rows to form all the elements are listed
separated by comma enclosed whether
for example one two three four five six
they are also made by comma enclosed by
braces this is the set describing or
numbering attacks also 8io you separated
by comma enclosed within braces this
will present set of all vowels and
English alphabet
second point willing to notice that the
order in which the element are listed is
immaterial order is immaterial for
example when we say AEIOU or these
workers in uniform it does all see now
when we say we have three dots at the
end that means that set continues
infinitely also in slow stir form the
elements are not repeated for example
when we say we want to form the set of
letters of the word school it is SCH o L
since o was twice in school but by
writing sets we wrote only once because
we avoid reputation it does not mean
that if you write an element words it
will be long this will be correct but
the carnation is that be chili bowl will
be the remains of rooster form in
set-builder form all the elements should
possess a single common property which
is not produced by any element outside
the set so you have to find a common
property common property is a very very
crucial thing if you have a set of
element which is not forming which is
not having a single common property then
you can't write that inside with the
form for example when we say setup
e-i-e-i-o you we know that this is all
father's in English alphabet so no other
element for example I say imply a big M
M will not have this properly said will
not have this property so no other
element no other English alphabet no
other letters will have properly so if
we get
set like this then only we can write the
accent in set-builder form for example
for the same set hey I owe you this is a
rooster form why it is watch perform
because all the elements are listed
separated by comma and enclose my
embrace now for the same goes to form
said if you want to write in set-builder
we will do something like this you say
set is you can do curly wicked shot X X
colon X and we'll write the property it
is something like this X and there you
see property so it sails this is the
convention so here X is above all an
illusion of it this is clear that in
set-builder common properties Magna tree
which is possessed by the elements in
the set and no other element I would say
intersect will handle property for
example when you say EERE you we have
you know these are all vowels and the
English alphabet and the way we
represent is X : and then see property
so here we say X : X is a government
lease alphabet now let's discuss some of
the important points which we have in
separate forms the first is instead of
later X which we have used we can use Li
and the later for example we can see by
Y is a father you can do something like
this you should have X because they said
also can say said there is a father so
we need not to use X now this colon is
very much mandatory when you see let's
suppose when you say X the semi colon X
is a vowel this is wrong this colon is
very very mandatory this is must also
after the signing of column we write the
property so here Y is above all organism
oven this is the characters property
the limits of the sector and the I
enclose in the blesses this again the
fourth point which have already
discussed if the set does not follow any
pattern we can't write we can write
please note we can't write in
set-builder form that means any set we
can write in roaster form roaster form
is going to any set we can write any
scent and he said because we are jotting
the elements but in set-builder norm in
set-builder form pattern is a must only
pattern set pattern set D now let's take
some example of roaster former set
builder form will have will have a
position where in will ask whether with
the roaster power set built from to
clear our concepts on those Department
set will perform so when I say a X X is
an integer and X is greater than minus C
less than 7 fish vomit is obvious it is
a set built form because a set with a
form we have told that it is something
like X and here we see property includes
you the deliciousness so this satisfies
the condition so it is set builder pass
in a second question we say B 3 the set
X : X is the national number again we
see is follows the same pattern so this
is also set built upon C you say X X the
to G is not national number said that
some of it do the same again here we see
the elements has a common property that
is some of it is if this weight and it
is in the set builder form because it
says X : property inclusive racism let
us take an example of set D where we say
X : property and property is it is a
prime number and which is a division of
60 again it is a property so all the
remains which follow this property with
the part of the set now let us take an
example so this is a set
now E is a set where all the elements
are listed three six nine twelve so
since all the elements are listed
separated by comma enclosed in braces
this is nothing but personal form we
have discussed this in lotion form all
the elements are listed separately by
gamma enclosed in the basis if F is
again if you see all their events are
listed separated by comma in clothes
moving pieces so f is also roaster form
I hope you are getting the point
when all the elements are listed
separated by comma enclosed within
braces
it is roaster form and then we say X :
property this is also enclosed in braces
this is set bitter G G is 525 120 means
it should be fine here also since all
the elements are listed separated by
comma enclosed in braces so this is also
close to form similarly for H it says 2
4 6 dot dot dot as we remember this is
nothing but 2 4 6 8 10 12 14 16 there is
an infinite set so since all the
elements are listed separated by gamma
in tourism business so this is also
roaster form will take for example so in
this the 3 dots are in the centre and
200 so it is it means it is 1 4 is 2
square minus 3 square then it is 4
square Phi square continue still 10
square is hundred so it's continues till
10 swear if you see right here also all
the elements are listed separated by
comma and includes in braces curly
braces so it is also in roaster form so
if you see the first 4 where it says X
colon property they are in set builder
from writes and building from and the
last 5 where all the elements are listed
separated by comma improve the dresses
these are on postal form thank you
with it example
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