Types of Relations (Part 1)

Discrete Mathematics: Types of Relations
Topics discussed:
1) Reflexive relation definition and example.
2) Irreflexive relation definition and example.
3) Symmetric relation definition and example.
4) Anti-symmetric relation definition and example.
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*2 hour

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Much more short and straighforward explanation. Appreciated🌸

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Gm

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Concise and to the point. Thanks

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Your video is best one for relation examination

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Thanks sir , your way of explaining is fantastic

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FR

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This is very helpful

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[@MatthewViterbo0017]

This helped me alot. Thank You~

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Great 👍

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[@TinasheMunjeri]

Great work appreciated

[@JaneDoe-fm9jj]

question: why isn't there (1;3)??

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4:06 ....... Why we need not to check for (1, 1), (2, 2)

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[@gayathrik7673]

So a=b means it is not symmetric but anti symmetric?

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[@user-pg6uf6dz7o]

The first ex given for irreflexive relation is not irreflexive but is it reflexive or not

[@YfAsm17]

Is there any relation which is not reflexive, not irreflexive and not antisymmetric

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Topic explaination is very good

[@ross9263]

Holy shit I love you. My brain finally understands symmetric vs antisymmetric

[@zanelemileyshandu4876]

Hi I am not understanding the example on Antisymmetric, shouldn't it be that THAT example is NOT Antisymmetric?

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I am from India

[@saifabbasi3114]

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[@sidharthpg3900]

How is anti-symmetric different from non-symmetric?

[@Siva_Shyam]

Consider a relation R = { (1,1) , (1,2) , (3,1) , (1,3) } Here R is not symmetric because ,R is symmetric if there exists a,b then there should be b,a since R contains 1,2 but not 2,1 R is not symmetric However , R is also not Antisymmetric because , R is Antisymmetric if it contains a,b but not b,a ( note : it can have a,a as an ordered pair ) since in our example there exists 3,1 as well 1,3 which is not allowed in antisymmetric relation and Hence, Antisymmetric is not always equal to (not symmetric) I hope you got it!

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Sir can I conclude that antisymmetric is equal to not symmetric

[@Siva_Shyam]

No you cannot because , Consider a relation R = { (1,1) , (1,2) , (3,1) , (1,3) } Here R is not symmetric because ,R is symmetric if there exists a,b then there should be b,a since R contains 1,2 but not 2,1 R is not symmetric However , R is also not Antisymmetric because , R is Antisymmetric if it contains a,b but not b,a ( note : it can have a,a as an ordered pair ) since in our example there exists 3,1 as well 1,3 which is not allowed in antisymmetric relation and Hence, Antisymmetric is not always equal to (not symmetric) I hope you got it!

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[@AmitYadav-cx9ww]

if a relation is not irreflective .is reflective????

[@amberjha5974]

Not necessary, if some elements in a set are {a,a} and some are {a,b}, then its not reflective as {a,b} exists but it isn't irreflective either since {a,a} exists. It has to be all elements following the requirement.

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i haven't understand which you have explained its not clearly explain

[@Siva_Shyam]

Let me explain you, Antisymmetric = { (1,1) , (1,2) , (2,3) } Here if 1,2 ( say a,b ) exists then 2,1 ( that is b,a ) is not allowed , however if 1,1 ( say a,a ) exists then 1,1 ( agai a,a ) is allowed Assymetric = { (1,2) , (2,3) , (3,1) } Here if (a,b) exists then (b,a) is not allowed, also (a,a) is not allowed Consider a relation R = { (1,1) , (1,2) , (3,1) , (1,3) } Here R is not symmetric because ,R is symmetric if there exists a,b then there should be b,a since R contains 1,2 but not 2,1 R is not symmetric However , R is also not Antisymmetric because , R is Antisymmetric if it contains a,b but not b,a ( note : it can have a,a as an ordered pair ) since in our example there exists 3,1 as well 1,3 which is not allowed in antisymmetric relation and Hence, Antisymmetric is not always equal to (not symmetric) I hope you got it!

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DBMS

[@coryanders6328]

This explanation is illogical. How is something irreflexive because the numbers are not in the set when they are clearly in the set?

[@nithishnagendra]

Antisymmetric? never heard of that when i was studying PU i thought the last one was Transitive relations

[@Siva_Shyam]

Let me explain you, Antisymmetric = { (1,1) , (1,2) , (2,3) } Here if 1,2 ( say a,b ) exists then 2,1 ( that is b,a ) is not allowed , however if 1,1 ( say a,a ) exists then 1,1 ( agai a,a ) is allowed Assymetric = { (1,2) , (2,3) , (3,1) } Here if (a,b) exists then (b,a) is not allowed, also (a,a) for a

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[@farooqhusain5534]

anti symmetric is not clearly explained makes no sense or logic

[@Siva_Shyam]

Let me explain you, Antisymmetric = { (1,1) , (1,2) , (2,3) } Here if 1,2 ( say a,b ) exists then 2,1 ( that is b,a ) is not allowed , however if 1,1 ( say a,a ) exists then 1,1 ( agai a,a ) is allowed Assymetric = { (1,2) , (2,3) , (3,1) } Here if (a,b) exists then (b,a) is not allowed, also (a,a) is not allowed Consider a relation R = { (1,1) , (1,2) , (3,1) , (1,3) } Here R is not symmetric because ,R is symmetric if there exists a,b then there should be b,a since R contains 1,2 but not 2,1 R is not symmetric However , R is also not Antisymmetric because , R is Antisymmetric if it contains a,b but not b,a ( note : it can have a,a as an ordered pair ) since in our example there exists 3,1 as well 1,3 which is not allowed in antisymmetric relation and Hence, Antisymmetric is not always equal to (not symmetric) I hope you got it!

[@headyshotta5777]

you shouldve had images to represent the relations in this video. all the formal notation is brain melting. no thanks

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[@gayathrik7673]

So a=b means it is not symmetric but anti symmetric?

[@Siva_Shyam]

No you cannot because , Consider a relation R = { (1,1) , (1,2) , (3,1) , (1,3) } Here R is not symmetric because ,R is symmetric if there exists a,b then there should be b,a since R contains 1,2 but not 2,1 R is not symmetric However , R is also not Antisymmetric because , R is Antisymmetric if it contains a,b but not b,a ( note : it can have a,a as an ordered pair ) since in our example there exists 3,1 as well 1,3 which is not allowed in antisymmetric relation and Hence, Antisymmetric is not always equal to (not symmetric) I hope you got it!

[@zaifansari3044]

❤️