What is relation in Math Video Lecture | Additional Study Material for Class 12

we are learning lessons and functions in
mathematics and so far we have already
discussed two other pair and Cartesian
product between two sets and now we're
going to introduce a new topic that is
relationship or simply you can say
relation in mathematics this relation we
need very nicely while we will be
learning function in for the chapters
all right you might be wondering
relation in mathematics and I will say
yes release in mathematics and even I
will surprise you that this relationship
is exactly like the day to day
relationship in our daily life right
let's say for a while I have a family
all right let's see I have a family this
is my imaginary family all right let's
say this is my family for a while and
I'm going to make two group alright
Group A and Group E right group a
contains the name of husband and Group B
contains the name of wife all right fine
happy okay so in the first group I'm
going to try the members let's say
father all right and then grandfather
and then brother and okay that that's it
and this is one group of husbands and
I'm going to make a group of wife now
dad so definitely there should be mother
grandfather then there should be
grandmother also and brother then there
should be sister-in-law and my sister
but my sister is unmarried it and do you
know my friend my grandfather is married
with two women so he has two wives and I
have two granny
all right so grandmother one and
grandmother too let's say granny - all
right so I have here two groups one is
for husband another is for wipes and now
I'm going to make a relationship between
the group a and Group E and the name of
the relationship I am giving our and it
is in such a way that now in a pair
actually I'll make a pair all make
couples I will choose some couple here
in such a way that X is husband of of Y
okay where X is from first group and Y
is from second group all right so how
many such pairs I can find out let me
check it up father
yes father is the husband of
mother grandfather is the husband of
grandmother but this grandfather is
married with two granny okay and brother
is married with with with with with the
sister-in-law so this is relation in
mathematics also my dear friends and in
mathematics even we say like the the
element of this first group you know we
see this as a domain alright keep in
mind these are called domain and the
group second group in which relationship
has been built up this is called Co
domain and in Co domain if you see there
are few members or maybe all are in
relationship with the domain members of
domain are like mother get in
relationship with father grandmother
girl relationship with grandfather
sister-in-law got in restive with this I
mean sister is left here so those who
are in relation like mother grandmother
one sister-in-law and granny too so
these these members of core domain which
are in relationship with the members of
domain are called range all right so
range may be all Co domain or may be few
members of codomain so from here easily
I can say that range is a subset range
is a subset of Co domain keep this name
in your mind properly the first group is
called domain from where distance if it
starts and where listens if end up
that's calcio domain and few members
which are in relationship with the
domain members are called range okay and
now let's talk about the representation
of relationship in mathematics generally
we follow three method first one is
arrow diagram method and row diagram
method which is just here arrow diagram
method sometime we should balloon method
also just like this we need you know
swing with arrow which member is related
with which one this is collateral
diagram method second one is called
set-builder method which is here you
know we represented a relation from set
a to be you know like this as it is
written here and third one is a roster
method let me show you by the roster
method roster method is just giving us a
set you know so is a set of this
relation hmm and we know that father and
mother so far and mom writing in sort
right so father and mother for a short
similarly grandpa in short I am writing
where am I writing grandfather grandpa's
radio with granny 1 similarly grandpa's
related with a granny 2 and similarly
brother is created with with
sister-in-law right so this is our our
relationship you know and in this way if
you are representing our relations and
that's called roaster method right so
arrow diagram method which is here set
builder method which is here this one
and the roaster meter which is here and
you know my dear friend just I remember
we have already learned the other pair
and Kardashian products so we can
understand the relation in a Cartesian
product way also so friends here we have
a relationship for a while I'm just
going to remove this then what you're
going to get here just tell me yes
you're just getting some other pair you
know other pyramids it's reminding me
always the Cartesian product so if you
see end up in the state a there are
three members and inside B one two three
four five there are five members all
right so total a Cartesian product of a
cross B will be having 3 into 5 that is
15 members and those 15 members will be
some somehow like this let me show you
like father mother and then father and
granny granny - it's a it's a cardinal
Kardashian product it's not relationship
all right and so on like this you know
and at last you will get like rather
granny - so they're only 15 such members
all right and if you see this
relationship father mother grandparents
1 granny grandpa granny - brother sister
these this one two three four this four
members will be here also I'm going to
say a cross B will be having all those
members which are here all right so all
the members of this relationship will be
inside this a crispy right so
relationship is inside the a cross B I'm
going to say relationship is yes the
subset of Cartesian product of those two
set that is what I was trying to inform
you all right I'm just trying to deliver
that relationship is a special subset of
Cartesian product of those two set
definition in short we can say a
relation is subset of Cartesian product
of two non-empty sets so simply a
relation is a subset relation is a
subset of Cartesian product of two
nonempty sets so two nonempty set here
we have the set a and set B and there
are so many members in Cartesian product
a to be there are 15 members just we can
find out by multiplying the total
numbers from sate a and say PR right
like here we have 3 here we have 5 so 3
into 5 15 members there are and those 15
members from those 15 members we can
create so many subsets and those subsets
will give us the different different
type of the relation depending on the
definition of the relation alright how
we are defining so however we are
defining those all members in those any
relation that we are going to create
according to our definition will be from
a cross B only so every member of the
relation is inside the a cross B that's
what I want to see all right
so simply one more time let me revise
you our relation is a subset of a
Cartesian product of two nonempty set
and the first set is called domain
second city is called codomain where
recessive is build up and those members
of codomain which are in relationship
are called range and sometimes we say
these are ranged as image also alright
this is also called image alright and we
can read like we can read like this
mother is the image of father
grandmother is the image of grandfather
similarly sister-in-law is the image of
brother like that you know so this is
how relationship is and we're going to
learn furthermore a lot about
relationship and you're going to get
more and more concept of relationship I
hope you understand this and if there is
any more confusion any doubt about this
relation then please feel free to
comment below this video I'll definitely
get back to you and please don't forget
subscribe the channel and hit the like
button to this video bye bye