Hasse diagram, minimal elements, maximal elements
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Given $A = {2, 4, 6, 8, 10, 16, 18, 24, 36, 72}$, and given the ordered set $(A, |)$, where $|$ denotes the relationship of the divide between natural numbers.
• Draw the Hasse diagram of $(A, |)$.
• Determine all the minimal and maximal elements, and any minimum and maximum of $(A, |)$.
• Determine:
$inf_A {16, 18} =$
$sup_A {4, 6} =$
My attempt:
Minimal element: $2$
Maximal element: $72$
Minumum: $2$
Maximum: doesn't exist
I don't know how to calculate $inf_A {16, 18}$ and $sup_A {4, 6}$.
discrete-mathematics
asked Jan 21 '18 at 17:00
JonsaJonsa
135
$endgroup$
add a comment |
$begingroup$
Given $A = {2, 4, 6, 8, 10, 16, 18, 24, 36, 72}$, and given the ordered set $(A, |)$, where $|$ denotes the relationship of the divide between natural numbers.
• Draw the Hasse diagram of $(A, |)$.
• Determine all the minimal and maximal elements, and any minimum and maximum of $(A, |)$.
• Determine:
$inf_A {16, 18} =$
$sup_A {4, 6} =$
My attempt:
Minimal element: $2$
Maximal element: $72$
Minumum: $2$
Maximum: doesn't exist
I don't know how to calculate $inf_A {16, 18}$ and $sup_A {4, 6}$.
discrete-mathematics
asked Jan 21 '18 at 17:00
JonsaJonsa
135
$endgroup$
$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03
add a comment |
$begingroup$
Given $A = {2, 4, 6, 8, 10, 16, 18, 24, 36, 72}$, and given the ordered set $(A, |)$, where $|$ denotes the relationship of the divide between natural numbers.
• Draw the Hasse diagram of $(A, |)$.
• Determine all the minimal and maximal elements, and any minimum and maximum of $(A, |)$.
• Determine:
$inf_A {16, 18} =$
$sup_A {4, 6} =$
My attempt:
Minimal element: $2$
Maximal element: $72$
Minumum: $2$
Maximum: doesn't exist
I don't know how to calculate $inf_A {16, 18}$ and $sup_A {4, 6}$.
discrete-mathematics
asked Jan 21 '18 at 17:00
JonsaJonsa
135
$endgroup$
Given $A = {2, 4, 6, 8, 10, 16, 18, 24, 36, 72}$, and given the ordered set $(A, |)$, where $|$ denotes the relationship of the divide between natural numbers.
• Draw the Hasse diagram of $(A, |)$.
• Determine all the minimal and maximal elements, and any minimum and maximum of $(A, |)$.
• Determine:
$inf_A {16, 18} =$
$sup_A {4, 6} =$
My attempt:
Minimal element: $2$
Maximal element: $72$
Minumum: $2$
Maximum: doesn't exist
I don't know how to calculate $inf_A {16, 18}$ and $sup_A {4, 6}$.
discrete-mathematics
discrete-mathematics
asked Jan 21 '18 at 17:00
JonsaJonsa
135
asked Jan 21 '18 at 17:00
JonsaJonsa
135
edited Jan 21 '18 at 17:04
Jonsa
asked Jan 21 '18 at 17:00
JonsaJonsa
135
asked Jan 21 '18 at 17:00
JonsaJonsa
135
asked Jan 21 '18 at 17:00
JonsaJonsa
135
135
$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03
add a comment |
$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03
$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03
$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03
add a comment |
1 Answer
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You left out the edge (24, 72). The infimum is the smallest element that divides both 16 and 18, namely 2, an the supremum is the largest element divisible by both 4 and 6, namely 72.
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
$endgroup$
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I don't understand how to draw it correctly
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– Jonsa
Jan 21 '18 at 17:41
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"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
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Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
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– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
add a comment |
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1 Answer
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1 Answer
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active
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$begingroup$
You left out the edge (24, 72). The infimum is the smallest element that divides both 16 and 18, namely 2, an the supremum is the largest element divisible by both 4 and 6, namely 72.
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
$endgroup$
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
add a comment |
$begingroup$
You left out the edge (24, 72). The infimum is the smallest element that divides both 16 and 18, namely 2, an the supremum is the largest element divisible by both 4 and 6, namely 72.
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
$endgroup$
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
add a comment |
$begingroup$
You left out the edge (24, 72). The infimum is the smallest element that divides both 16 and 18, namely 2, an the supremum is the largest element divisible by both 4 and 6, namely 72.
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
$endgroup$
You left out the edge (24, 72). The infimum is the smallest element that divides both 16 and 18, namely 2, an the supremum is the largest element divisible by both 4 and 6, namely 72.
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
answered Jan 21 '18 at 17:06
saulspatzsaulspatz
15.6k31331
15.6k31331
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
add a comment |
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
I don't understand how to draw it correctly
$endgroup$
– Jonsa
Jan 21 '18 at 17:41
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
"You left out the edge": are you referring to the Hasse diagram?
$endgroup$
– Jonsa
Jan 21 '18 at 17:42
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Yes there, there should be a line from 24 to 72.
$endgroup$
– saulspatz
Jan 21 '18 at 17:46
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
Is this correct? ibb.co/joFE6w
$endgroup$
– Jonsa
Jan 21 '18 at 17:52
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
$begingroup$
No. Why did you add a line from 8 to 18?
$endgroup$
– saulspatz
Jan 21 '18 at 18:07
add a comment |
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$begingroup$
24|72 Once you add the edge for this, $sup(4,6)=72$
$endgroup$
– saulspatz
Jan 21 '18 at 17:03