Mixing
If ∀A ∈ PX , ∀B ∈ PY , |A| < |B| Then ∃A ∈ PX , ∃B ∈ PY , A ⊂ B
$begingroup$
X and Y are non-empty sets , X c Y (subset ) and Px is a partition of X and Py is a partition of Y .
How can I prove that this statement is true or false :
If ∀A ∈ PX, ∀B ∈ PY ,|A| < |B|
Then ∃A ∈ PX, ∃B ∈ PY , A ⊂ B
Thank you .
Ps: what I understood is that since XcY then A that belongs to X belongs to Y as well and since the cardinality of A is smaller than B then A is likely to be a subset of B . My guess is this statement is true but I have no idea how to prove it , which method to use ? I don’t know how to start my proof .
discrete-mathematics
asked Feb 1 at 18:26
soso xoxososo xoxo
85
$endgroup$
add a comment |
$begingroup$
X and Y are non-empty sets , X c Y (subset ) and Px is a partition of X and Py is a partition of Y .
How can I prove that this statement is true or false :
If ∀A ∈ PX, ∀B ∈ PY ,|A| < |B|
Then ∃A ∈ PX, ∃B ∈ PY , A ⊂ B
Thank you .
Ps: what I understood is that since XcY then A that belongs to X belongs to Y as well and since the cardinality of A is smaller than B then A is likely to be a subset of B . My guess is this statement is true but I have no idea how to prove it , which method to use ? I don’t know how to start my proof .
discrete-mathematics
asked Feb 1 at 18:26
soso xoxososo xoxo
85
$endgroup$
add a comment |
$begingroup$
X and Y are non-empty sets , X c Y (subset ) and Px is a partition of X and Py is a partition of Y .
How can I prove that this statement is true or false :
If ∀A ∈ PX, ∀B ∈ PY ,|A| < |B|
Then ∃A ∈ PX, ∃B ∈ PY , A ⊂ B
Thank you .
Ps: what I understood is that since XcY then A that belongs to X belongs to Y as well and since the cardinality of A is smaller than B then A is likely to be a subset of B . My guess is this statement is true but I have no idea how to prove it , which method to use ? I don’t know how to start my proof .
discrete-mathematics
asked Feb 1 at 18:26
soso xoxososo xoxo
85
$endgroup$
X and Y are non-empty sets , X c Y (subset ) and Px is a partition of X and Py is a partition of Y .
How can I prove that this statement is true or false :
If ∀A ∈ PX, ∀B ∈ PY ,|A| < |B|
Then ∃A ∈ PX, ∃B ∈ PY , A ⊂ B
Thank you .
Ps: what I understood is that since XcY then A that belongs to X belongs to Y as well and since the cardinality of A is smaller than B then A is likely to be a subset of B . My guess is this statement is true but I have no idea how to prove it , which method to use ? I don’t know how to start my proof .
discrete-mathematics
discrete-mathematics
asked Feb 1 at 18:26
soso xoxososo xoxo
85
asked Feb 1 at 18:26
soso xoxososo xoxo
85
edited Feb 1 at 21:40
soso xoxo
asked Feb 1 at 18:26
soso xoxososo xoxo
85
asked Feb 1 at 18:26
soso xoxososo xoxo
85
asked Feb 1 at 18:26
soso xoxososo xoxo
85
85
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
X = { 1,2,3,4,5,6 }.
Y = { 1,2,3,4,5,6,7 }.
PX = { {1,4}, {2,5}, {3,6} }.
PY = { {1,2,3}, {4,5,6,7} }.
What does that example show?
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
$endgroup$
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
add a comment |
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1 Answer
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active
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1 Answer
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active
oldest
votes
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oldest
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active
oldest
votes
$begingroup$
X = { 1,2,3,4,5,6 }.
Y = { 1,2,3,4,5,6,7 }.
PX = { {1,4}, {2,5}, {3,6} }.
PY = { {1,2,3}, {4,5,6,7} }.
What does that example show?
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
$endgroup$
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
add a comment |
$begingroup$
X = { 1,2,3,4,5,6 }.
Y = { 1,2,3,4,5,6,7 }.
PX = { {1,4}, {2,5}, {3,6} }.
PY = { {1,2,3}, {4,5,6,7} }.
What does that example show?
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
$endgroup$
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
add a comment |
$begingroup$
X = { 1,2,3,4,5,6 }.
Y = { 1,2,3,4,5,6,7 }.
PX = { {1,4}, {2,5}, {3,6} }.
PY = { {1,2,3}, {4,5,6,7} }.
What does that example show?
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
$endgroup$
X = { 1,2,3,4,5,6 }.
Y = { 1,2,3,4,5,6,7 }.
PX = { {1,4}, {2,5}, {3,6} }.
PY = { {1,2,3}, {4,5,6,7} }.
What does that example show?
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
edited Feb 2 at 1:27
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
answered Feb 2 at 1:15
William ElliotWilliam Elliot
9,1562820
9,1562820
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
add a comment |
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
$begingroup$
Thank you that helped me see that A is not necessary a subset of B
$endgroup$
– soso xoxo
Feb 2 at 2:52
add a comment |
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