Proving $forall x forall y Rxy therefore forall x forall y Ryx$.
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
add a comment |
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
edited Dec 9 '18 at 4:36
dantopa
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
edited Dec 9 '18 at 4:36
dantopa
6,46942243
edited Dec 9 '18 at 4:36
dantopa
6,46942243
edited Dec 9 '18 at 4:36
dantopa
6,46942243
6,46942243
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
142
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
2
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
1 Answer
1
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oldest
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$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
$endgroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
edited Dec 8 '18 at 20:17
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
65.5k449113
65.5k449113
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
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$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12