Example of Roster and Set Builder Form - Sets Video Lecture - Class 11

hello friends this video set part please
brought you by exam fear calm before
watching this video you should have
bought sets part 1 and part 2 now let's
take one example they will convert
rooster form to set-builder form and
vice versa you get suspended positions
in the exams so we'll cover this so we
have an example where we say X is a
positive integer so X is we just observe
down here X is going to integer that is
positive so what are the positive
integers positive integers are 0 1 0 is
not a positive answer 0 is not positive
and 0 is also not negative so 0 is one
number which is neither positive nor
negative
so please note this this is little
tricky when you see a positive number 0
is included not not including when you
see a negative number then also given
over so 0 is neither positive nor
negative
so here when you say I plus it is a plus
then we have 1 2 3 4 continue still in
height so this is set of X so let's let
me write this set set X is this much now
on that we are having one more condition
that X is less than 4 so when you say X
is less than 4 4 is not less than 4
there is not only one two three are the
elements which are less than 4 1 is less
than 4 yes 2 is less than 4 yes 3 is
less than 4 yes 4 is less than 4 no so
let's talk here so the number of element
is 1 2 3 now when I want to write this
in roasted form what I have to do is you
have to write this all the limits
comma-separated eat close with the
bristles and then say e is equal to so
this is the answer to 3 now we have
pushed wherein we say we have to convert
this in the roaster form so we have X
square plus X minus 2
is equal to zero we have to convert this
in those two amounts in most around what
we do we write our elements all elements
listed if you remember in those two punk
or elements they said so first let me
know down all the elements so this is
the equation will solve this X square
plus 2x minus X minus 2 is equal to 0 or
we say X plus 2 into X minus 1 is equal
to 0 or X is equal to minus 2 or ma 1 so
these are the two sets so when you say
right dissolves in shape for equation is
in roster form then what we do we write
all the elements called elements are 2 &
1
sir by comma includes in braces and then
we see a is equal to this this is the
answer now let's take one more example
pardon my spelling this is our OST here
so I mean our OST is wrong so here it
says X is positive integer and X square
is less than 30 so when we say X square
is less than 31 square you see this
derivative X 1 is a positive integer so
first say what a positive integer so
positive integer is 1 to say 0 0 the
possibilities are known as we discuss
the 0 is neither positive nor negative
so we have 1 2 3 4 5 6
these are PI plus all positive integers
right now let us see the first element 1
square as in 30 yes 2 square is less
than 30 two squares building for less
than 30 years 2 3 square is less than 33
square is 9 is in 13 true 4 square is
less than 34 square this Steve doesn't
30 years true v square is thousand 30
yes to 5 squares 25 6 square is thousand
36 square is 30
so so we'll stop here if you want we can
do one more seven square thousand 37
square is 49 we'll stop here so the
elements we want this one to six no six
is also not any one two five one two
five this is the Liberty one so if you
want to write this in the most reformed
it goes perform again I say all elements
is then separated by car so we will say
K is going to write all the limits one
two three four five all are separated by
comma integral embraces so this is the
answer this is the roster form now let's
convert this into set built form so if
you see this set has element I and D e
so now I want to convert this into
second to convert this into simpler form
I have told that a rule is mandatory
there should be a rule which is strictly
followed by these elements so if you
observe clearly they're all letters or
word India I is there n is there D there
are you
similarly we can also say these are all
letters of word in the end right because
for Indian also these are all members of
Indian or we can say these are all
member of die not D are you see D is
member of this eizember this of e any
and all the way purse up there so we can
create so many use like this for a given
set for a given certain goes perform we
can have n number of answers instead so
we can write this set as
set a is equal to X where X is later of
what if they are we can also say a is
equal to X X is letter of word DN you
getting a point we can also say X X is
letter of word die now in fact you can
find n number of such words you can find
n number of such words for which I and
DA are the wheelie letters you can say
it is nd nd is the name of a guy so you
can say nd also so you can use any in E
but one time to say is for a given set
in poster form you can have n number of
answers so all these are correct answers
actually all the right answers because
re resist creating a rule and each of
these rule is particularly following the
curvature let's take for example so here
we have letters 1 2 3 6 9 game we have
to write it set builder bomb again the
first thing was that written comments
they should be able the first thing that
should come to our mind when we see such
question is what is the pattern what is
the pattern that these numbers are all
important in cases will read we have to
find the matter once people the pattern
is very easy to y-intercept send to the
phone so if you also tell me these are
all factors of 18 so
you see factors of 18 factors of 8 is
going to one who is a microwave in
freezer microwave e6 into fries 1892 is
a
80210 there are all factors of eating so
we have got them the rule is that all
participate so you can very easily write
this set a is equal to X where X is
factor of T so this is one answer I know
there may be a different answer for this
which you because if you look at this
word you may find a different part which
I am NOT able to find out if you are in
fine paddy for example the one we have
done in the last examples for int a we
found so many patterns one pattern world
these are all alphabets of word any
second pattern was they are all
alphabets of Indian third pattern was
they all over bits of China whole
pattern was they are also red shift and
E they can be n number of patterns so we
have n number of answers similarly for
this the only button
I knew was that they are factors of 18
serve and don't know yes and I know is
and there this is the answer but if you
know either button similarly let's take
for example so this number we have to
write in set-builder form again first it
will deform you're looking for the rule
we are looking for a pattern so let's
see the but what is the part mother's so
the pattern here I could see is all the
number here are described this you get
25 for example when you square minus 5
minus 5 whole square is equal to 25 then
you square 5 and what if it is anyway
this is the pattern I could see so I can
say that this set a is equal to X where
X square is equal to 80
this is again Z let's see one more
example we have someone 1 2 3 6 9 13 15
17 18 they have to write this instead
build upon again start with self or set
builder form we have to find a pattern
let's search for a pattern the pattern 1
2 3 6 9 14 15 17 18 these are not if you
see factor of 18 17 is there that means
this there is not factor of 18 so let's
take some more pattern any number less
than 18 so we have a lesser rate you
should be wanting to see but if you see
here 4 is missing Phi is missing so
again this was not pardon if you see
that real operating at will have it in
is 1 2 3 & 6 9 ET and here 30 50 or
extra so this is all not pardon
so we see that there is no pattern at
least I can't find a pattern so I will
declare that can't be written in 7 so
this is an example of a roaster form
which can't be written in simple form
because we are not able to find a model
if you are not able to find a pattern
that means you can't write that most of
all people set filter bar here we have
set a which has two element March and
May we have to write in set-builder form
as explained earlier and as we have seen
we have to find a pattern to write any
set in set-builder form we have to find
items let's find a pattern for this
monster and me so we see that these two
are months of year let's write down all
the month of here
so that you can find the pattern because
we have no clue you know what this March
maize so let's say Jan
femme April May June July August
September October November and December
these are the month of per year so what
we see is then the month which starts
with M R M March and me only
they are no other months we'll start
with M so we have on the button the
modernist X X is month of year starting
with you
they move this is a pattern we have form
so we can say set a is equal to X where
X is a month of year starting in them
and this is our answer friends please
don't to find you convert any row strip
on the set will form we have to find a
pattern so we found the button here that
these two ones are those ones these two
months are those months that start with
M thank you with it exam clear calm to
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