Relations and Functions Examples (NCERT) (Part -1) Video Lecture | Mathematics (Maths) Class 12 - JEE

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sure that you have watched part 1 2 part
8 example we have to show that relation
in the set 1 2 3 is given by 1 1 2 1 2 2
3 3 1 2 & 3 reflection but not symmetric
or larger so if there is set e which has
value 1 2 3 we could be Jerry get across
it and that will have value 1 comma 1 1
comma 2 1 comma 3 comma 1 comma 3 3
comma 1 3 comma 2 and 300 Watts all
right this value will get as part of a
cross now you will get a subset of this
a part of relation so in relation we'll
have some values 1 comma 1 2 4 1 2 3 4 3
1 comma 2 and you promise so this values
are nothing but when relation I got this
relation as this now to prove that it is
reflexive but not symmetric or not I
told reflection is reflection reflection
of a guide the reflection of yourself
that means if even exists even gamma
even exists that so you see if one
exists or the number one common exists
too common to exist 3 3 comma feels so
all the elements in this set are for to
the event ei gamma a is correct 1 comma
1 hukumat you to know so it is if let's
say done now whether it is symmetric or
not but symmetric I told if evil come by
it will exist then a 2 comma
even should also exist now you see what
do exist but you one is not
correct one two is there but is not
there so if you see this is not if you
just find one instance where one - is
there - where is on the uptick in this
also - 3 is there 3 2 is not there this
is not supported similarly but
transitive
I told you if even it will exist in - it
really exist then we have to confirm
that even in fish it also exists for all
accounts so you see here 1 comma 1
exists number starting with 1 is 1 comma
2 exists the fail we can take this 1 3
will take 123 action so one common to
exist number starting it will this will
link to here - 3 exists so each of bond
this you get 1 3 1 3 doesn't exist so if
you see this statement is falsified here
even it will exist it will exist but
even if a is not there so this is not so
please note it don't see that 1 comma 1
exists I take this value and I take 1
gamma 2 exist it's a goes and if you
watch this you get 1 comma 2 all exist
you can't say that it is positive
because even if one clear is there for
this this statement is false that means
this is not example there are 10
scenarios out of 10 9.2 that means all
existing that only one scenario where it
doesn't exist that means the whole
relation is not possible for
relationship to be transit this has to
be true God any three elements in the
set similarly for reflexive and symmetry
sorry let's take one more example we
have to show that relation in the set Z
of integers
are we where who divides a - wheels and
equivalence relation now for relation to
be equivalence it has to be reflexive
symmetric and transitive
first we'll prove that this or reflects
if I told it's a mirror reflection that
means we'll take a for my that is a
combination exists for all a but all
where is nothing but in Ian's is it
because we are talking about set of
integers and we are taking any event II
take on my goodness
now the questions 8 2 divides a kowai
who divides a comma a - a comment that
is a - leap over to see a car - a there
is 2 divides 0 yes 2 divides it for any
a on any a there is integer 2 divides 0
a minus a 0 so that means we can see
that this is reflexive one part of the
second is symmetric symmetric says that
if even if we exist then a to a velocity
that means if I say that if 2 divides
this is element even it even - because
it is a resilient even a - that means 2
divides the luminosity that implies 2
also divides into by this here correct
one if a 1 minus a 2 is 4 a 2 minus mu
minus 1 start so if this divides 2 this
will also be mainstream if you do - even
when a 0 is 5 and then a 2 - am i - 5 it
does not divide this also this is true
for for this possibly true for - me
because if you see a 2 minus a 1 or
just a side business - oculus but the
number is same so if a number is divided
by even - with you it will be divided by
eight - you also so this is seven click
this part is also short now the third is
transit for transit they right hold that
if even a - instance and you is resist
that implies if even need to exist in 83
in place that implies a 1 a 3 should
also exist for example if you see now if
I say you who divides even - quickly and
I say - divides 8 - if V because this to
exist this by default it implies who be
why it's even - it why I get X example
let's suppose a 1 a 1 is 1 this is 5 and
this one decibels man I mean 5 - 1 4 4
by 2 possible 9 - 5 4 possible for a by
2 impossible so you know if you take 9
minus 1 this will be if you take the
even sense to take this - it says this
it was 4 is 6 4 - to do you give rise to
possible 6-4 to device you possible 6-2
divide super awesome because see if you
take either odd or or all even in any of
this case are - orders even even
menacing in the city so even number will
be divided by so this becomes conclusion
that this
because putting any number even a to
easy any real this verse if even - Katie
divides to an A two months into words -
in a month we think that's all
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