Prove that in a boolean lattice, if $(a)le(b)$ then $($~$a)ge($~$b).$ [closed]












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discrete-mathematics order-theory lattice-orders







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closed as off-topic by amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ Nov 26 at 19:48


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ

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  • What is your guess? How is $le$ defined?
    – Berci
    Nov 26 at 17:08










  • Boolean lattice: a lattice which is complemented and distributed.
    – aj14
    Nov 26 at 17:10












  • a<=b means b covers a
    – aj14
    Nov 26 at 17:13
















-2














Statement may be correct or wrong, give proof in either case.






discrete-mathematics order-theory lattice-orders







share|cite|improve this question















closed as off-topic by amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ Nov 26 at 19:48


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ

If this question can be reworded to fit the rules in the help center, please edit the question.













  • What is your guess? How is $le$ defined?
    – Berci
    Nov 26 at 17:08










  • Boolean lattice: a lattice which is complemented and distributed.
    – aj14
    Nov 26 at 17:10












  • a<=b means b covers a
    – aj14
    Nov 26 at 17:13














-2












-2








-2


1





Statement may be correct or wrong, give proof in either case.






discrete-mathematics order-theory lattice-orders







share|cite|improve this question















Statement may be correct or wrong, give proof in either case.






discrete-mathematics order-theory lattice-orders




discrete-mathematics order-theory lattice-orders






share|cite|improve this question















share|cite|improve this question













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edited Nov 26 at 17:12

























asked Nov 26 at 17:03









aj14

12




12




closed as off-topic by amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ Nov 26 at 19:48


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ

If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ Nov 26 at 19:48


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ

If this question can be reworded to fit the rules in the help center, please edit the question.












  • What is your guess? How is $le$ defined?
    – Berci
    Nov 26 at 17:08










  • Boolean lattice: a lattice which is complemented and distributed.
    – aj14
    Nov 26 at 17:10












  • a<=b means b covers a
    – aj14
    Nov 26 at 17:13


















  • What is your guess? How is $le$ defined?
    – Berci
    Nov 26 at 17:08










  • Boolean lattice: a lattice which is complemented and distributed.
    – aj14
    Nov 26 at 17:10












  • a<=b means b covers a
    – aj14
    Nov 26 at 17:13
















What is your guess? How is $le$ defined?
– Berci
Nov 26 at 17:08




What is your guess? How is $le$ defined?
– Berci
Nov 26 at 17:08












Boolean lattice: a lattice which is complemented and distributed.
– aj14
Nov 26 at 17:10






Boolean lattice: a lattice which is complemented and distributed.
– aj14
Nov 26 at 17:10














a<=b means b covers a
– aj14
Nov 26 at 17:13




a<=b means b covers a
– aj14
Nov 26 at 17:13










1 Answer
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The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0














    The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
    $$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$






    share|cite|improve this answer


























      0














      The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
      $$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$






      share|cite|improve this answer
























        0












        0








        0






        The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
        $$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$






        share|cite|improve this answer












        The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
        $$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 26 at 17:23









        Berci

        59.5k23672




        59.5k23672















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