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
asked Nov 26 at 17:03
aj14
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closed as off-topic by amWhy, user10354138, Brahadeesh, Mostafa Ayaz, TravisJ Nov 26 at 19:48
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- "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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up vote
-2
down vote
favorite
Statement may be correct or wrong, give proof in either case.
discrete-mathematics order-theory lattice-orders
asked Nov 26 at 17:03
aj14
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.
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
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Statement may be correct or wrong, give proof in either case.
discrete-mathematics order-theory lattice-orders
asked Nov 26 at 17:03
aj14
12
Statement may be correct or wrong, give proof in either case.
discrete-mathematics order-theory lattice-orders
discrete-mathematics order-theory lattice-orders
asked Nov 26 at 17:03
aj14
12
asked Nov 26 at 17:03
aj14
12
edited Nov 26 at 17:12
asked Nov 26 at 17:03
aj14
12
asked Nov 26 at 17:03
aj14
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
add a comment |
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
add a comment |
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
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$
answered Nov 26 at 17:23
Berci
59.2k23672
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$
answered Nov 26 at 17:23
Berci
59.2k23672
add a comment |
up vote
0
down vote
accepted
The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$
answered Nov 26 at 17:23
Berci
59.2k23672
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$
answered Nov 26 at 17:23
Berci
59.2k23672
The complements are unique in a distributive lattice, moreover $sim(alor b)=sim a landsim b$, so we have
$$ale biff alor b=biff sim a landsim b=sim biff sim agesim b$$
answered Nov 26 at 17:23
Berci
59.2k23672
answered Nov 26 at 17:23
Berci
59.2k23672
answered Nov 26 at 17:23
Berci
59.2k23672
answered Nov 26 at 17:23
Berci
59.2k23672
59.2k23672
add a comment |
add a comment |
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