Group in Discrete Mathematics with examples in Hindi

A group is a monoid with an inverse element.

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►For Any Query, Suggestion or notes contribution:

[safaltiwari]

sir in case of natural no, with operation multiplication, it is not a group
8 *(1/8)=1
but here 1/8 is not natural no.
so it is not a group

[nabiel]

(N, *)is not a group
Becoz
5*1/5=1
But 1/5 does not belong to N

[sreepooja]

Sir, please please upload the rest of the videos. Your videos are conceptual and easy to understand. 🥺

[irfanhussain]

Your teaching experience is totally different from others LOVE FROM KASHMIR

[rajendrakumarshaw]

(N, ×) is closure, semi-group, also monoid, but it is not a group, because 1/N is not a natural number, inverse doesn't exist.

[gitanshagarwal]

It is algebraic structure, semigroup and monoid but If we take 5*(1/5)=1 then though we obtain the identity element but as (1/5) is not a natural number and hence it doesn't belong to the set of natural numbers and so it is not a group.

[muhammadather]

As usual very easy to comprehend. Bravo 👍

[ramankumar]

Sir your explanation is very clear....Huge Thanks to You Sir.

[kalpanaverma]

Yeah !!! That's the content which I am looking for ! Thank you so sooo much sir ..

[manishajoshi]

Ur explanation is very clear & easy to understand ....thanks 👍😊

[whatssay]

a*(1/a)=1 but 1/a doesn't belong to natural number

[shubhsharma]

For [N, . ],

First checking if its AG, Closure: Yes, the product of two natural numbers is always a natural number.

then checking if its a semi group or not with associativity: Yes, multiplication is associative.

Now checking if its a monoid with Identity element: Yes, the identity element is 1, because for any natural number n, n * e = n, so 1.

Now checking if its a group or not with inverse element:

No because not every natural number has a multiplicative inverse within the set of natural numbers. Because

lets take a = 4 then, a * b = 1, 4 * b = 1 then b = 1/a which is not possible in N so

[N, . ] is not a group.

[annukamboj]

Nice session sir👍👍, , Discrete k sbi topic complete krwa do sir please for NET exam...

[RohiniSabale-xqpx]

(N, .)is an algebric structure,
it is a semigroup,
it is monoid,
but it is not a group

[allgoodcontents]

Sir there is a one request, please upload the vedio on the topic Floyd's algorithm for all pairs shortest path problem .... I have seen this topic from various other channels but I'm not able to understand this topic from there. please sir i want and need ur explanation in this topic.... I know you will surely make this vedio sooner.... Thank you

[moviestaataion]

sir (N, . ) IS not a grp becoz if 5 is taken then in indentity 1 we have to take 1/5 which is not an natural no.

[sidmission]

Sir in (R, *) case in group we can multiply with 1 instead of 1/n

[jayeshsinh]

Varun sir, how many is needed to complete a discrete mathematics.from your videos??

[anahataghosh]

conceptual, concrete, concise. thank you, sir

[tanish__]

Sir (N, •) is not a group because of most of number ke inverse element N me nhi hai 🙏🏻