Example Symmetric Transitive (Part - 13) - Relations and Functions, Maths, Class 12 Video Lecture

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relations and functions part 12 it's
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video please make sure that you have
watched part 1 to part 12
take some more example here again we
have to determine the relationship like
zip 17 transitive relation R in the set
Z of all integers defined as X y when x
minus y is an integer you see this this
also will try to find without real
number set actually in this case we
can't find it significant because the
integers are huge huge number of
integers difficult to find the real
number set so what we can do is we can
just try using the common sense we'll
try with the reflexive for reflexive
what I told a comma M should be their
correct echo my reflexive is your own
mirror reflection we were standing you
are standing here also and it supposes a
mirror that's how it is so that means X
comma X should exist X comma X exists X
comma X is nothing but X minus X this
integer X minus X is nothing but 0 and 0
is an integer we know that since zero is
integer we can say that it is reflexive
for any value of x X minus X is integer
so we can see that this is reflexive so
this is love for symmetry what I don't
if a 1 a 2 exists this should imply a 2
even correct so if even a to exist
this means a 1 minus a 2 is integer it
even minus a 2 is integer we can say
that - of a1 minus a2 is also integer if
number is integer negative button so
sensor or we can say that a 2 minus a 1
is also integer if a 2 minus a 1 is
integer
well we can say that a tu cama even is a
member of see what had done even into is
integer that this a1 a2 is a member of
the set this implies a1 minus a2 is an
integer this also implies minus of a 1
minus a 2 is also integer correct
because negative of integer is an
integer and this is nothing but a 2
minus a 1 minus of even - 80 s of your
ATM - signals integer if my over 2 minus
a 1 is an integer this means that a 2
comma even is a member of this set so it
is symmetric also let me Norma
transitive whatever do what transit if
you hadn't proved that if even into is
member and into a 3 is member this
should imply that even a 3 is awesome
now if even a double let's suppose we
take X Y Z or even to even it is member
this a 1 minus a 2 is integer kind this
implies this and this implies into minus
a three integer both are true statements
if you add both these statements both of
India you add two integers so if you add
these two what again even minus k2 this
is a teacher a 2 minus a 3 this is also
a teacher if you add too windy just you
get index is only you say canceled live
in a van - 80 and that is also
interested so from these 2 I can
conclude that a 1 minus a 3 is also in
teacher
how come here minus 80 was integer a 2 -
III was integer since these are two
integers if I add two integers I give
India here so I got a one - III Z pigeon
if even - a this integer that means even
Parma a three is member of this since
even from Isis member of this said this
means it is not correct you solve this
question without finding the
relationship very simple for reflexive
even even reasoning
member yes for symmetric a 180 is a
member implies a to a will say member to
submit but rather take even into is a
member a 2 a 3 is a member this implies
a 1 a 3 7 1 if this holds true that
means this is transit let's check on my
zap here we have read the mind and the
relation is reflexive symmetric and
transitive where is the set of human
beings in a town so this is nothing but
a usually have some human beings feel
awesome some human makes in a town this
guy there's a first of all a small V
small V small D NR so the first s
relation where x and y work at the same
place the second is where next exactly 7
centimeter taller than Y and the third
relation is where X is the Y of Y for
all these to e be able to determine
whether this is reflexive symmetric or
transitive so first links take 1 for
this reflexive now we have been fined
for the collection for the Flexi but I
told it's a mirror reflection if X comma
X exists that means it is reflexive for
all the elements in the set so if X
comma X that means X and X work at the
same place that is true because we don't
even see in gun this guy and this guy
hey Andy go to the same place correct so
it is true so it is reflexive so I say
reflexive is secant is the symmetric for
this for symmetric what I told for
symmetric if XY is there this will imply
YX also right if XY is the part of
relation z Y X should also be the part
of traditional say that P is if x and y
work at the same place and YX a
why and x1 at the same place for the
same shape if I say a and B will get the
same place or I say V and they work at
the same place both are same so it is
symmetric also for transitive I told X Y
exists requires it is this it should
imply X comma Z in this case if I say
that x and y work at same place it
suppose x and y over bits and is second
I say Y & Z work at same place correct
this automatically implies that X and Z
also look at the same place logically it
is true right so if x and y are working
at the same place why I ended up walking
in the same place that is all are
working in the same place right since
they are also working in the same place
that means it is transitive also so this
relation on the set of people human
beings walking in the same town is
reflexive symmetric and climb now I will
go for the second relation you please
note the set a is all saying the same a
has all the human beings in it now the
only thing you are changing in the
relation and that is what is making a
difference now the new relation see is
that this is gone so put in the brace
you see the new relation see is that X
is exactly 7 centimeter taller than Y so
for the Flex if I told X and X it exists
so if I take X and X that means X is 7
centimeter taller than X that is not
possible
because one guy can't be sevenths and
given Tarzan himself so it is not
reflexive for symmetric I told if X Y
exists Y X would also exist so X Y is
this that means X minus y 7 that is X 7
sin it was in Y if Y exists Y X exists
this is this thing so we have to say
that Y minus X is equal to 7
that is why is 7th
the next this is not possible if X
guy-guy X is taller than Y by 7 Cindy
Whitner
he can't be shorter than that way right
she is guys X is taller it is guys legs
this guy's why this guy is taller than X
or than Y we can say X minus y is going
to say but the reverse will not be true
so insipid trick I taught you to flip it
in this case flipping is not working so
it is not possible for transitive but I
told if X Y exists Y there exists X
sensor should also exist so assume X Y
difference is 7 this suppose this guy is
20 so this guy is 30 again this is a guy
called Z and that guy's is 6 so if you
see X Y exists because the difference
between x and y is 20 minus 13 it is 7
so XY exists why is it exists because
the different between y&z is 7y and
there is is but now if you take x and z
the different reason X that is how much
20 minus 6 that ends for you so in the
difference is 14 it is not 7 so this is
not part of this set that means this
exists this exists but X comma Z will
not exist in this relationship and that
means it is not even transitive you
understand this what I've done I assume
XY exists I assume was it exists with
that I got the hypothetical figures and
then I found it X Z will not exist
because the difference is in X then Z is
not 7 centimeter so this part is also
done where we found that it is neither
transitive
nor symmetric norm now the third
relation x is the wife of Y again for
reflexive if you see that X for my X
exists that means it is reflexive but a
person can be can't be by himself right
this guy can be this girl can be wife of
this guy so one girl can be wife of
himself and one guy can be your wife on
system this is not possible this is
impossible scenario so reflexing is not
part of this sick and is say for
symmetry it sees that if XY exists Y X
should exist that means if I am saying
that X is y of Y this should imply that
Y is y Eve of X that is incorrect
because if X is y 4 y Y is actually
husband of X naught Mike of X so this is
not existing flipping is not working
here flipping is not working here so it
is not even seven thing similarly now X
is y for transitive
now let's go for transitive but turn on
the divider if X Y exists why is it
exists so x-jet suppose exists so I am
saying that X is wife of Y that is XS
remain and Y's mean if wise main this
guy will not be I have a mini one with
this relation itself only question
saying X is y equal Y so Y is made so
why can't be 5 of any man so this view
won't even get this one this is the
difference story all together that means
this is not monitored okay so what do
you observe for the same set a sometimes
we got around the tip sometimes if flex
yet sometimes symmetric based on the
relationship we eat thank you visit exam
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