Show the logical equivalence of $p to q to perp$ and $p wedge q to perp$. [on hold]
I'm asked to show the logical equivalence of $p to q to perp$ and $p wedge q to perp$. When I make the truth tables, the two statements seem to come out to two very different outcomes, perhaps I'm interpreting the question wrong and the answer is that they aren't logically equivalent?
propositional-calculus
edited yesterday
metamorphy
3,5721521
asked yesterday
Richard Cameron
11
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put on hold as off-topic by Mauro ALLEGRANZA, amWhy, José Carlos Santos, KReiser, Shailesh yesterday
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, José Carlos Santos, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
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I'm asked to show the logical equivalence of $p to q to perp$ and $p wedge q to perp$. When I make the truth tables, the two statements seem to come out to two very different outcomes, perhaps I'm interpreting the question wrong and the answer is that they aren't logically equivalent?
propositional-calculus
edited yesterday
metamorphy
3,5721521
asked yesterday
Richard Cameron
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Mauro ALLEGRANZA, amWhy, José Carlos Santos, KReiser, Shailesh yesterday
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, José Carlos Santos, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
3
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday
add a comment |
I'm asked to show the logical equivalence of $p to q to perp$ and $p wedge q to perp$. When I make the truth tables, the two statements seem to come out to two very different outcomes, perhaps I'm interpreting the question wrong and the answer is that they aren't logically equivalent?
propositional-calculus
edited yesterday
metamorphy
3,5721521
asked yesterday
Richard Cameron
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm asked to show the logical equivalence of $p to q to perp$ and $p wedge q to perp$. When I make the truth tables, the two statements seem to come out to two very different outcomes, perhaps I'm interpreting the question wrong and the answer is that they aren't logically equivalent?
propositional-calculus
propositional-calculus
edited yesterday
metamorphy
3,5721521
asked yesterday
Richard Cameron
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
metamorphy
3,5721521
asked yesterday
Richard Cameron
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
metamorphy
3,5721521
edited yesterday
metamorphy
3,5721521
edited yesterday
metamorphy
3,5721521
3,5721521
asked yesterday
Richard Cameron
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Richard Cameron
11
asked yesterday
Richard Cameron
11
11
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Richard Cameron is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Mauro ALLEGRANZA, amWhy, José Carlos Santos, KReiser, Shailesh yesterday
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, José Carlos Santos, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Mauro ALLEGRANZA, amWhy, José Carlos Santos, KReiser, Shailesh yesterday
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, José Carlos Santos, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
3
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday
add a comment |
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
3
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
3
3
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday
add a comment |
1 Answer
1
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oldest
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First, note that $x to perp = lnot x lor perp = lnot x$. So
$p wedge q to perp = lnot(p land q)$
$(p to q) to perp = lnot(p to q) = lnot(lnot p lor q) = p land lnot q$
$p to (q to perp) = p to lnot q = lnot p lor lnot q = lnot (p land q)$
So, as pointed out in the comments above, it all depends where you put the parentheses when you interpret $p to q to perp$.
answered yesterday
gandalf61
7,703623
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
First, note that $x to perp = lnot x lor perp = lnot x$. So
$p wedge q to perp = lnot(p land q)$
$(p to q) to perp = lnot(p to q) = lnot(lnot p lor q) = p land lnot q$
$p to (q to perp) = p to lnot q = lnot p lor lnot q = lnot (p land q)$
So, as pointed out in the comments above, it all depends where you put the parentheses when you interpret $p to q to perp$.
answered yesterday
gandalf61
7,703623
add a comment |
First, note that $x to perp = lnot x lor perp = lnot x$. So
$p wedge q to perp = lnot(p land q)$
$(p to q) to perp = lnot(p to q) = lnot(lnot p lor q) = p land lnot q$
$p to (q to perp) = p to lnot q = lnot p lor lnot q = lnot (p land q)$
So, as pointed out in the comments above, it all depends where you put the parentheses when you interpret $p to q to perp$.
answered yesterday
gandalf61
7,703623
add a comment |
First, note that $x to perp = lnot x lor perp = lnot x$. So
$p wedge q to perp = lnot(p land q)$
$(p to q) to perp = lnot(p to q) = lnot(lnot p lor q) = p land lnot q$
$p to (q to perp) = p to lnot q = lnot p lor lnot q = lnot (p land q)$
So, as pointed out in the comments above, it all depends where you put the parentheses when you interpret $p to q to perp$.
answered yesterday
gandalf61
7,703623
First, note that $x to perp = lnot x lor perp = lnot x$. So
$p wedge q to perp = lnot(p land q)$
$(p to q) to perp = lnot(p to q) = lnot(lnot p lor q) = p land lnot q$
$p to (q to perp) = p to lnot q = lnot p lor lnot q = lnot (p land q)$
So, as pointed out in the comments above, it all depends where you put the parentheses when you interpret $p to q to perp$.
answered yesterday
gandalf61
7,703623
answered yesterday
gandalf61
7,703623
answered yesterday
gandalf61
7,703623
answered yesterday
gandalf61
7,703623
7,703623
add a comment |
add a comment |
Which values of $p$ and $q$ did you take to get the "two very different outcomes"?
– 5xum
yesterday
3
Where are parentheses ? In order to anwer correctly, you have to put them...
– Mauro ALLEGRANZA
yesterday
We have that $lnot (p to q)$ is equivalent to $(p land lnot q)$
– Mauro ALLEGRANZA
yesterday
And also that $(p to lnot q)$ is equiv to $lnot (p land q)$.
– Mauro ALLEGRANZA
yesterday
You need brackets to identify what goes with what. When you are combining binary operators which need not be associative, this is crucial.
– Mark Bennet
yesterday