x∈ (AUB)' X∉(AUB) X∉A and X∉B My question is, why the U in second line interprets for 'and' in the second line. As we know, union is interpreted for 'Or'. Same is the question for the ∩ in the proof of (A∩B)' where it is interpreted for 'Or'.
it is because , when an element does not belong to a set then the way the sign is expressed changes for eg- if x does not belong to AUB , THEN IT WILL BE EXPRESSED AS x does not belong to A and B
The set for intersection of A and B includes the elements which are common in both A and B and x can be an element in either set without being a common element of both sets. For union of A and B,all elements of both sets are included meaning that if x does not belong to this set then it does not belong to both sets A and B
@@azeezahmad8850 okay thanks for the union part explanation but what about the intersection part. that if Y doesn't belongs to(A int B) then how can we say that (Y doesn't belongs to A) *and* Y doesn't belongs to B)
@Violater since x doesn't belong to A intersection B that means x can be element which can be in A OR in B this statement can be written as x is not a element of A, then it is in B OR x is not a element of B, then it is in A To represent this he wrote x not belongs to A or x not belongs to B
How can you justify saying that x is is not an element of A or B in the intersection one? You said x is an element of the complement of A intersection B which means x is apart of a universal set that does not include any shared elements of A or B. However if A or B has elements that are not shared then those can still be in the universal set as the complement was of their intersection, not the entire sets A and B. And x is an element of that complement, so it could still be one of the elements in A or B. I say "or"; "and" in normal English.
Yes then it won't be considered as Intersection of the Set A & Set B .we are concerned with Intersection of (A & B ), lefts one's may be in A or B or in U . In at particular Instance, If there is anything in BOTH SETS ,mean that They Can't be Out of The BOTH SETS ,at same Instance.
Very good explanation. Only thing though is that when you use this proof, it only means that one set is included in the other, not necessarily meaning that the two sets are equal.
Sir, Could please explain how are you writing "or" when it is intersection. It means "And". Ok, which principal is applied to change "and" into "or" directly.
@@faridsahraouiii It's because of that “not” If x does “not” belong to the A intersection B, then there are two possibilities(cases): 1) x doesn't belong to both A and B (meaning x belongs to complement of A intersection B) 2) x doesn't belong to either A or B (meaning x belongs to complement A or x belongs to complement B) If we use the 1st possibility (infact we already have done it), then we'll get complement of ‘A intersection B’ instead of complement A union complement B, which we have to prove.
bhai proper steps k sath prove krna hota h sir , aapne bs baate ghuma kr conclusion la diya...aapne bs smjhaya h but proper steps se prove krna nhi sikhaya........exam mai agr aise prove kra to marks nhi milenge
In the first part you are using 'and' instead of the union symbol and instead of the intersection symbol, however we should use 'or' instead of the intersection symbol. Am I missing something?
Sir for the third step of the first proof why the word " and" not "or" ? Bcoz "and" means it belongs to both the sets which means it belongs to the intersection while here we want to show it belongs to the union so it should be X doesn't belong to A" or ".....B
Step 2: x does not belong to A or B. Step 3: x is not in A and it is not in B also We are not saying that it is not in the intersection of A and B Hope that makes sense. Thanks
In the first round, how does the the union just suddenly become and ? because i thought union means or and intersection means and as later discussed in the video
Yes, you're right. ‘or’ means union & ‘and’ means intersection... But when you're dealing with ‘not’, then you need to be careful with cases. A union B has three parts - A intersection B and two difference of sets; mathematically it is represented as A∪B = (A-B)∪(A∩B)∪(B-A) So if x does ‘not’ belong to A union B, there is a case where A doesn't belong to A intersection B... Infact, you don't need to do these all, even with thinking logically, you'll realise that by your own like this: (A-B), (B-A) and (A∩B) are subsets of A∪B so If x doesn't belong to A∪B then simply x also doesn't belong to any of them since they're subsets of A∪B and now use that (A∩B) and write x doesn't belong to A “and” x doesn't belong to B.
While the first section is ok, second section does not seem to make sense.... Or am I getting it wrong? How is it that x NE of A -OR- x NE of B, should it not be x NE of A -AND- x NE of B so x could be element of A, then it is not an element of B, and x could be an element of B, but then it cannot be an element of A However, the theorem could be still proved, as if x is NE of A, then it is assumed to be element of A Complement. Similarly, if x is NE of B, then it is element of B Complement. so x surely will be in A Comp Union B Comp
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dude explained the shit in the best way anyone could, truly grateful
ikrr
x∈ (AUB)'
X∉(AUB)
X∉A and X∉B
My question is, why the U in second line interprets for 'and' in the second line. As we know, union is interpreted for 'Or'.
Same is the question for the ∩ in the proof of
(A∩B)' where it is interpreted for 'Or'.
it is because , when an element does not belong to a set then the way the sign is expressed changes
for eg-
if x does not belong to AUB , THEN IT WILL BE EXPRESSED AS
x does not belong to A and B
@@aayuushmehta8133 you are just restating De-Morgan's Law in English rather than set theory notation... this makes the proof circular in nature
@@SrishDutta Thank you! I think the same, whats the deal with the guy going silent on the most important part of the proof.
The set for intersection of A and B includes the elements which are common in both A and B and x can be an element in either set without being a common element of both sets.
For union of A and B,all elements of both sets are included meaning that if x does not belong to this set then it does not belong to both sets A and B
@@azeezahmad8850 okay thanks for the union part explanation but what about the intersection part. that if Y doesn't belongs to(A int B) then how can we say that (Y doesn't belongs to A) *and* Y doesn't belongs to B)
CLEAR AND WITH PERFECTION THANKS
Thanks
you have a soothing voice and clear explanations. Thanks so much!
You did so good. wish profs explained it like this!
Best explanation of demorgans law ever
I agree with you 100%
Best teacher ever
Well explained
Best explanation of de Morgan's theorem on yt ❤️🙂
Correct
Yea wahi log hai ...jo ki aapna jaath dekh ke samajhte hai ki yahi #AMAZON_BASIN hai
♥️
Did you see all videos of Morgan's law ?!😒🥴
@@dearcontents 😯😯😯
Really thanks for the video!
Best explanation ever
Thanks
Wasn't in the class when written this proof now it seems i am ready for midterm test insha'allah .
THANK YOU ❤
@Violater since x doesn't belong to A intersection B
that means x can be element which can be in A OR in B
this statement can be written as
x is not a element of A, then it is in B OR
x is not a element of B, then it is in A
To represent this he wrote
x not belongs to A or x not belongs to B
thnk u sir 🙇🏻♀🙇🏻♀🤧🤧
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wonderful explanation and calming voice. Thank you sir😇
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thank you so much. bless you
Thanks
How can you justify saying that x is is not an element of A or B in the intersection one? You said x is an element of the complement of A intersection B which means x is apart of a universal set that does not include any shared elements of A or B. However if A or B has elements that are not shared then those can still be in the universal set as the complement was of their intersection, not the entire sets A and B. And x is an element of that complement, so it could still be one of the elements in A or B. I say "or"; "and" in normal English.
Yes then it won't be considered as Intersection of the Set A & Set B .we are concerned with Intersection of (A & B ), lefts one's may be in A or B or in U .
In at particular Instance, If there is anything in BOTH SETS ,mean that They Can't be Out of The BOTH SETS ,at same Instance.
Good
Very good explanation. Only thing though is that when you use this proof, it only means that one set is included in the other, not necessarily meaning that the two sets are equal.
Best explanation sir I love you yar you helped me
Thanks so much it was very helpful
Thanks
Sir I am not able to understand that why in a union b complement yu have written and . And in a intersection b complement yu have written or
Excellent proof
Better than others ❤
Thanks for the explanation sir
Best explanation of de Morgan's law. Thank you so much.
Thankyou so much sir ,today is my maths exam and I will sure do well 😊😌❣️
All the Best!
Same to same explanation is given in R.D. Sharma's 11th class book.
If anyone wants to see the full proof of the De-Morgan's Law.
Simple and precise 🤝
Sir I'm understand everything but in last step how to came union and intersection . Please tell about it
due to and used for union, or used for intersection
@@sidrapervaiz3409 but *and* is used for *intersection* and *or* is used for *union* right?
thank u sir
Why the union is written as and...?
Well xplained tenks ser😀😀
Sir,
Could please explain how are you writing "or" when it is intersection. It means "And".
Ok, which principal is applied to change "and" into "or" directly.
Same issue
A or B = Union
A and B = Intersection
Thanku sir....
It is very easy to understand
Nice, i was confused with "And" "or" thing.
Thank you bro 😅
very crisp sir
Thank you sirr ❤
Thanks. PLAYLIST for you: ruclips.net/video/HjT6G4_lqg4/видео.html
Very useful 🎓💯
You have assisted me alot
This solution may be wrong or incomplete or anything, but never be the right one.
I got everything but why {x: doesn't belong to (A Union B)}
Then how there's and in place of union sir
Make a Venn Diagram. That will help to visualise. Thanks
But if the x doesnt belong to the intersect of ab its should mean that it doesnt belong to both a and b or ( doesnt belong to one of them )!
Intersection in other words: It could belong to any one of them not both. Thanks
@@MathematicsTutor so what is union ,????? Belonging to both ?? Isnt union belonging to one of the sets or both?
@@faridsahraouiii It's because of that “not”
If x does “not” belong to the A intersection B, then there are two possibilities(cases):
1) x doesn't belong to both A and B (meaning x belongs to complement of A intersection B)
2) x doesn't belong to either A or B (meaning x belongs to complement A or x belongs to complement B)
If we use the 1st possibility (infact we already have done it), then we'll get complement of ‘A intersection B’ instead of complement A union complement B, which we have to prove.
APPRECIATED ♥️
Best explanation of DeMorgan's theorem .Very beneficial for me ...❤️
Best👍
Thank you ❤️
Sir you have only proved the condition of a subset .The proof is incomplete.
u r right
@@abhishekdiggal2433comment 4 yr ago 💀 and reply 4 month ago 🥬
We will do same for other half of give given question but in reverse order
Yes
Union of sets generally means 'or'. So in 1:27 why have you written 'and' instead of 'or' ?
True, Union is OR
@@MathematicsTutor sorry sir. I have understood.
Fabulous 😁
Thank you Sir you've made me understand 🤲🙏😊
bhai proper steps k sath prove krna hota h sir , aapne bs baate ghuma kr conclusion la diya...aapne bs smjhaya h but proper steps se prove krna nhi sikhaya........exam mai agr aise prove kra to marks nhi milenge
Fantastic work, Anil. Concise and easy to understand!
THANKYOU ❤️
Thanks for the best explaining in this video sir ❤
Thanks
thank you this helped
Awesome. It's could be never forgot
thank you so much for the explanation
Tq
In the first part you are using 'and' instead of the union symbol and instead of the intersection symbol, however we should use 'or' instead of the intersection symbol. Am I missing something?
I have the same question
I think wrong in or & And, please check well
Sir for the third step of the first proof why the word " and" not "or" ? Bcoz "and" means it belongs to both the sets which means it belongs to the intersection while here we want to show it belongs to the union so it should be X doesn't belong to A" or ".....B
Step 2: x does not belong to A or B.
Step 3: x is not in A and it is not in B also
We are not saying that it is not in the intersection of A and B
Hope that makes sense.
Thanks
მადლობა
Very beneficial For me...And Your way of teaching Is too Good Sir❤️
thnx sir
can some explain why x cannot belong to the union of a and b though ?
because x belongs to complement of a and b, so it is not belonged to the union. of a and b
Thank you so much sir .....
Why and is written in between?
U means 'or' ?
It's amazing and it's very easy to understand thanks 👍😊
In the first round, how does the the union just suddenly become and ? because i thought union means or and intersection means and as later discussed in the video
Yes, you're right. ‘or’ means union & ‘and’ means intersection... But when you're dealing with ‘not’, then you need to be careful with cases.
A union B has three parts - A intersection B and two difference of sets; mathematically it is represented as A∪B = (A-B)∪(A∩B)∪(B-A)
So if x does ‘not’ belong to A union B, there is a case where A doesn't belong to A intersection B...
Infact, you don't need to do these all, even with thinking logically, you'll realise that by your own like this: (A-B), (B-A) and (A∩B) are subsets of A∪B so If x doesn't belong to A∪B then simply x also doesn't belong to any of them since they're subsets of A∪B and now use that (A∩B) and write x doesn't belong to A “and” x doesn't belong to B.
Why am I learning this in 9th...
Great ! Great !
Thank you !
~Anurag Mishra !
Sir you have to consider the case when x not belongs to A union B
While the first section is ok, second section does not seem to make sense.... Or am I getting it wrong?
How is it that x NE of A -OR- x NE of B,
should it not be x NE of A -AND- x NE of B
so x could be element of A, then it is not an element of B, and x could be an element of B, but then it cannot be an element of A
However, the theorem could be still proved, as if x is NE of A, then it is assumed to be element of A Complement. Similarly, if x is NE of B, then it is element of B Complement. so x surely will be in A Comp Union B Comp
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Thank you good sir.
A very clear explanation. Thanks!
First you go and upload coding videos on your channel
Very nice explaination sir. I appreciate your clear voice.
Thanks
Perfectly awesome👍
Really appreciate work...u explained it too simple.... really i have no words👍🏻👍🏻sir
If you have any kind of problem in any subject so watch video
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Tqqqqqqq sir
Thank you Sir. I understood very easily within fewer minutes. Take Love From Bangladesh ❤️🇧🇩
Thanks for this❤️
The missing part is proving the tautologies ¬(A˅B)⇔¬A˄¬B and ¬(A˄B)⇔¬A˅¬B. But this is so simple I would leave it as an exercise to listener.
set equality proofs have to be proven in both directions right?
Thanku so much sir
Thank you very much for this explanation : ) greetings from Poland
In Poland is their also maths
@@samarsingh9480 and is there chutiya teachers like him there also😂😂
@@samarsingh9480 of course dude , everyone has to study maths , without Maths world can't exist
Can anyone give me a hand with this?
Let A and B two subsets of the universal set U={x:x∈ℤ and 0≤x
Intersection will be the null or empty set.
Union will be all the elements.
Hope that helps
Thanks
Click the link and comment your problem also watch video
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Short and accurate.., lovely
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Thanks
I can't understand yet
Which step is not clear. Please let me know. Thanks
Thank you very much Mr Anil Kumar for the powerful explanation of de Morgan's laws of sets. I have really understood.
Thank you so much for solving in a simple way. 😊
can't tell you how much our teacher dragged it!
Union means 'or' right?
Yes bro
union should be written as OR
Thanks soo much 😁
toma tu like
Thank you! I got it❤
Sir what is the meaning of \ this mark like BUA\CUA=BUC\A
AUB means x€a or x€b then why u all are speaking that x€a and x€b
Thanks. Union is OR and not AND.
Appreciate it
+Anil Kumar but why
@@bkshambhu2533 Right I also didn't get that