L6 : Transitive Relations - Relations and Functions, Maths, Class 12 Video Lecture

hello friends this video on relations
and functions part six is brought you by
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before watching this video please make
sure that you have watched part 1 to
power five has two symmetric and
reflexive let's try to understand the
third complex 10 information that is
transitive relation as a word
transitive means transitive means you
move from one first place to on the base
you start from a you moved in this place
will you please see that is the meaning
of transitive something that moves up so
they are three of I can say pause or
place there's a guy-guy name is program
the flag moves from A to B and then he
moves from B to C so finally what we
have seen Rohith has moved from this
point hold this correctly so he moves
from A to B and then we do see that
doesn't make it up transitive easy you
have this in your mind then you can
understand transitive relation in a
better way now that it means the person
moves from A to B and then we do see so
mathematically burden if you see a
relation is called transitive if a
veneto let's suppose if a 1 comma a was
part of the set
correct also if a you come I 3 is part
of the set that should imply that a 1
and a 3 is also find so this is the game
of Marco please long gears are positive
if a relation in relation is changed to
be transitive if and only if if you find
that ever it is part of set also a2 a3
is part of set the relationship the VAR
set in that case even a 3 has to be part
of the so if that is true then fully
that particular relation is part
transitive relation right C to get a
relation for example forgetting relation
of a only thing all the objects of a mu
C plus a look at some
some items from this items based on
relation greater than equating height is
noble height is there some some time
later some pattern you get subset on
this you get a subset and you get this
relation in this relation if you see
even a - is there a - a - is there and
also a OHP is there then that relation
is one transitive relation if what these
are there and this is not there then
this is not wrong a connection explain
for example so if I say height of boys
are Nexian examples single example so
let the height of OS be generating ad
now I say height of a1 is equal to
effective ad that is one set height of
a2 is equal to Phi 2 V 3 this implies
height of a visible light is acting to a
tree boys hair when laying in this guy
is v1 this is v2 v3 and this guy is it
so if I see that height of or I polite
even is equal to ad which is one thing I
go then I told a tree is going to Italy
the second thing I do then this I apply
that even is equal to height of paper
has various this such kind of tradition
exists then this kind of relation is
called one function so in case of equal
to relation this is the contribution and
I'm saying height of a one is going to
80 and it is vertically then that
implies height of Abel is also 4 really
correct so in this case if you see what
they have done height of a1 is equal to
a2 that was there and don't we do spend
to a3 also there but this we have seen
that height of evil is going to go to
the 4 y equal X so all these three of
this are there for installation so this
kind of relation is gone
transitive I'll give an example of non
trans regulation makes loud clear
example I say height of a ver is not
equal to Omega naught equal to is my
relation here in Olivia's it was equal
to relation now I am taking about not
the correlation
so in that case if I'm saying that
height of a one they suppose the height
of this guy is small centimeter the
again fine
and this time three now all it supposes
for only actually this is one until you
identically now when I say that height
of a is not equal to even is not equal
to do it is four five will form up a
super buy them form up here Cignetti
height of a to is not equal to a 3
this guy will was a compact it was the
height are not equal so 500 also found
this should imply the Hat so what for
should also be the part of relation but
for 4 means the height of this is not
equal to I to this but they are equal so
this is not part of a set the only
element in this set this this and this
so this is Amala not just white for was
this because if we take 3 this becomes
out talkative but even if there is one
element there is there is one element
which can make this whole set not on the
tape then this the record not so
generally not equal to spot non ones
because there may be a case there may be
a case where this guy's height is say if
you are given the exact height then by
unity now you can say where the set the
strong even when the tape in the exact
head is not mentioned please say please
mention not equal to relation as
non-transitive also also the greater the
relation is also non constant and then
examples to divide so let's suppose let
us give the name here I say v1 v2 v3 and
v4 usernames of all these poor boiz so
this is example of less than
Beaverhead is less than we do cut
similarly the people height is less than
V T this implies
we even height is definitely this will
be true for orders all the case so here
you see less than is a transitive
relation so less than and say less than
greater than are generally transitive
relation only not equal to our gently
contours the relation equality is also
classical because you flow from here V 1
is 11 V you we do a little this implies
V 1 s that means this relation is in the
same clears at the same relation
existence then there has to be same
relation between this to this if that
exists then it is called transit if you
see here the relation is flying from
here to here from here to here it went
from here to here it print that means
the relation from there to X and I am
saying that Y goes from A to B then we
do we see that means am saying oh I move
from A to C similarly relation between B
1 we do we do when we see in live
relation between internet D so that is
what we call positive relation thank you
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thanks again