Relations and Functions Examples (NCERT) (Part - 2) Video Lecture | Mathematics (Maths) Class 12 - JEE

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functions part 11 is brought you by exam
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sure that you have watched part 1 to
part tension says we have determined
whether the relation defined by from set
a we have our X Y where 3x minus y is
equal to 0 holds true this relation is
reflexive symmetric and transitive
the first thing L do is we have to first
find the elements that is the first
thing if you can jot down the elements
that will be part of this set because R
will be nothing but a subset of a cross
a do this let us put the value of x to
be 1 inch we keep on doing it so we'll
get some values of y so input X go to 1
3 X minus y is equal to 0 or you get Y
is equal to nothing but 3x X is equal to
1 Y is how much 3 into 1 3 if you put X
is equal to 2 what you get Y y is 2 into
3 6 similarly if you put X is equal to 4
you will get Y is nothing but 3 into 4
that is 12
I miss X equal to 3 so let me put that
if you put X equal to 3 you get Y is
equal to 3 into 3 that is my this you
got X divide 3 into pull that is 6 and
this you got 3 into 1 that is if you put
X equal to 5 you get Y is equal to 3
into 5 that is 15 and 15 is not part of
this set because the number maximum is 1
to 14 so if you put things go to 6 you
get Y is equal to 80 that is also not
part of the set so this is the maximum
value of x that we can have for the
element to be in this set so the element
in this set will be X comma Y that is 1
comma 3 1 comma 3 comma 6
the next element for cover - well in the
next element 3 comma 99 is next element
if I conclude is not there so only four
elements are there as part of this
relation so relation has for element 1
comma 3 2 comma 6 4 comma 12 and 3 comma
9 now the first question is whether the
set is the reflexive or not but it flex
if I told a combination exists that is 1
comma 1 2 comma 2 3 compound 3 4 comma 4
like this so you see 1 comma 1 is not
there in this 2 comma 2 is not there
none of this is there so we can say that
it is not touch less correct so this
reflexive is it for symmetric I told if
a verb comma E - is there a 2 comma a 1
has to be there then it is symmetric so
if you see 1 3 is there but 3 1 is not
there correct for symmetric I told even
in - is there that implies
into a van should be there but what we
have observed is 1/3 is there there but
3-1 is not there so it is not symmetric
correct it is not even symmetric the
third is transitive or transitive as I
showed you the boy was moving from point
A to B then from a B to C so I showed
that if a my 2 is there and a 2 a 3 is
there this should imply a 1 III should
be there
correct so you see here we take 1 3 + 3
9 then one pay regard so you take 1 3 +
3 9 so that this implies 1 a 1 is this
one and really is this one so you get 1
mine should be the implied value so one
mine should be there in part of this set
but if you see one line is not there 1 3
is there few 9 is there but one - not
there since 1 is not there we can see
that this settles not even positive so
what we have seen we have seen that this
relation is not transitive not symmetric
not so what are they approaching forward
the first thing we did was based on this
relation 3x minus y is going to 0 and
from this set we got the elements in
this relation once we have the four
elements in this relation it is very
easy to find whether the relation is
reflexive symmetric and 1 let's take up
my example in this p.m. little mind the
relation is again the Flex is symmetric
or 12 even now the relation is defined
as set of national number are in this
relation is y is good 2x plus 5 where X
is less than 5 so if you see national
number national number starts from 1 it
goes to 2 3 4 5 6 to infinity correctly
now the relation R is defined as X comma
Y and the value of x can be less than 4
so the value of x is 1
for the three possible value of x
because this all values are greater than
equal to one so I have X can have three
values and say 1 comma 2 or mine you
come up and why what is the value of y
is nothing but X plus 5 so X is going to
1 y is nothing but 1 plus 5 that is 6
this becomes X to Y becomes T plus 5
that is 7 and X is equal to 3 y becomes
3 plus 5 that is 8 so I got these 3
pairs in this relation so this relation
has 3 elements 1 comma 6 comma 7 and
click on first part is done now I have
to find whether it is reflexive for
reflects if I told what the reflection
is nothing but mirror so for the Flex if
a comma a element should be there that
is 1 comma 1 2 comma 2 3 comma 3 4 comma
4 all the elements should be there but
if you see 1 gamma 1 is not there so it
is not reflexive correct this is not
look like for symmetric I told you
symmetry you imagine the least the flip
thing box that does if even a to exist
this shouldn't lie into a one should
also exist
so you see 1 6 is there but 6 1 is not
there you see 1 6 is there but 6 1 is
not there since 6 1 is not there you can
say that it is not even trade so
symmetric also ruled out the third
option is transitive for transitive
alright or if a 1 a 2 there a 2 a 3 is
there this implies that a 1 a 3 is also
there so let's take one scenario 1 comma
6 6 comma something 6 comma something
itself
1 comma 2 comma 70 inaudible to make the
player itself correct so we can say that
it is not wrong
it is not a bit wrong because for
positive 1 comma 6 is there then 6 comma
some numbers and exists N and then 1
comma n should also exist but that is
not there so we can say that it is not
even so what we have done then is
simpler the first thing we did was we
just got the elements in this relation
regard that there are three elements in
this relation and then once we have the
element in the relation we can easily
find whether it is reflexive symmetric
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