How do you prove B v A |- A v B?

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I am having trouble with how to use the assumption, which I feel that I will need for this proof.

If any one can demonstrate or give hints for this proof, I would greatly appreciate it.

logic symbolic-logic

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edited 4 hours ago

Frank Hubeny

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up vote
2
down vote

favorite

I am having trouble with how to use the assumption, which I feel that I will need for this proof.

If any one can demonstrate or give hints for this proof, I would greatly appreciate it.

logic symbolic-logic

share|improve this question

edited 4 hours ago

Frank Hubeny

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asked 5 hours ago

MoIsStillHere

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MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
2
down vote

favorite

up vote
2
down vote

favorite

I am having trouble with how to use the assumption, which I feel that I will need for this proof.

If any one can demonstrate or give hints for this proof, I would greatly appreciate it.

logic symbolic-logic

share|improve this question

edited 4 hours ago

Frank Hubeny

4,4153938

asked 5 hours ago

MoIsStillHere

183

New contributor

MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

I am having trouble with how to use the assumption, which I feel that I will need for this proof.

If any one can demonstrate or give hints for this proof, I would greatly appreciate it.

logic symbolic-logic

logic symbolic-logic

share|improve this question

edited 4 hours ago

Frank Hubeny

4,4153938

asked 5 hours ago

MoIsStillHere

183

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MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|improve this question

edited 4 hours ago

Frank Hubeny

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asked 5 hours ago

MoIsStillHere

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share|improve this question

edited 4 hours ago

Frank Hubeny

4,4153938

edited 4 hours ago

Frank Hubeny

4,4153938

edited 4 hours ago

Frank Hubeny

4,4153938

4,4153938

asked 5 hours ago

MoIsStillHere

183

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asked 5 hours ago

MoIsStillHere

183

asked 5 hours ago

MoIsStillHere

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183

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2 Answers
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oldest

votes

up vote
1
down vote



accepted

Here is a proof using Klement's proof checker and rules provided in forall x. These may or may not be adequate, but they offer one way to go about proving this.

The premise or assumption is in line 1 and the conclusion or goal is in line 6. The proof checker starts off by writing the assumption for me. You would simply state it on line 1 if you are not using a proof checker. In the reference section is the link to the proof checker that I am using. You may use as well for future exercises as a way to check if your proofs are correct.

Since the premise is a disjunction (an "or" proposition), I need to consider two cases. The first case, "B", I considered in lines 2 and 3. The second case, "A", I considered in lines 4 and 5. I need to get the same result in both cases to invoke the disjunction elimination (∨E) rule, which I did on line 6. Note that I had to use the disjunction introduction (∨I) rule on lines 3 and 5. Since it did not matter which order I used I used the order I needed for the goal.

You may be required to use other rules or other names for the rules than the ones I used.

---

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

add a comment | 

up vote
2
down vote

Let's discuss the intuitive meaning of B∨A. It means either B or A.

If that is the case then, writing any disjunct first or last should not truth functionally matter.

Now, let's go to the truth table:

B A (B∨A) (A∨B) 
T T T T
T F T T
F T T T
F F F F

As you can see the corresponding truth values are identical and therefore, (A∨B)≡(B∨A).

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

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Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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• 
  
  
  

  
  

  
  
  
  
  
  

  
  I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
  – Frank Hubeny
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @FrankHubeny Thank you for the edit, That is precisely how I wanted it.
  – Bertrand Wittgenstein's Ghost
  3 hours ago
  

  
  
  
  

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

Here is a proof using Klement's proof checker and rules provided in forall x. These may or may not be adequate, but they offer one way to go about proving this.

The premise or assumption is in line 1 and the conclusion or goal is in line 6. The proof checker starts off by writing the assumption for me. You would simply state it on line 1 if you are not using a proof checker. In the reference section is the link to the proof checker that I am using. You may use as well for future exercises as a way to check if your proofs are correct.

Since the premise is a disjunction (an "or" proposition), I need to consider two cases. The first case, "B", I considered in lines 2 and 3. The second case, "A", I considered in lines 4 and 5. I need to get the same result in both cases to invoke the disjunction elimination (∨E) rule, which I did on line 6. Note that I had to use the disjunction introduction (∨I) rule on lines 3 and 5. Since it did not matter which order I used I used the order I needed for the goal.

You may be required to use other rules or other names for the rules than the ones I used.

---

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

add a comment | 

up vote
1
down vote



accepted

Here is a proof using Klement's proof checker and rules provided in forall x. These may or may not be adequate, but they offer one way to go about proving this.

The premise or assumption is in line 1 and the conclusion or goal is in line 6. The proof checker starts off by writing the assumption for me. You would simply state it on line 1 if you are not using a proof checker. In the reference section is the link to the proof checker that I am using. You may use as well for future exercises as a way to check if your proofs are correct.

Since the premise is a disjunction (an "or" proposition), I need to consider two cases. The first case, "B", I considered in lines 2 and 3. The second case, "A", I considered in lines 4 and 5. I need to get the same result in both cases to invoke the disjunction elimination (∨E) rule, which I did on line 6. Note that I had to use the disjunction introduction (∨I) rule on lines 3 and 5. Since it did not matter which order I used I used the order I needed for the goal.

You may be required to use other rules or other names for the rules than the ones I used.

---

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

Here is a proof using Klement's proof checker and rules provided in forall x. These may or may not be adequate, but they offer one way to go about proving this.

The premise or assumption is in line 1 and the conclusion or goal is in line 6. The proof checker starts off by writing the assumption for me. You would simply state it on line 1 if you are not using a proof checker. In the reference section is the link to the proof checker that I am using. You may use as well for future exercises as a way to check if your proofs are correct.

Since the premise is a disjunction (an "or" proposition), I need to consider two cases. The first case, "B", I considered in lines 2 and 3. The second case, "A", I considered in lines 4 and 5. I need to get the same result in both cases to invoke the disjunction elimination (∨E) rule, which I did on line 6. Note that I had to use the disjunction introduction (∨I) rule on lines 3 and 5. Since it did not matter which order I used I used the order I needed for the goal.

You may be required to use other rules or other names for the rules than the ones I used.

---

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

Here is a proof using Klement's proof checker and rules provided in forall x. These may or may not be adequate, but they offer one way to go about proving this.

The premise or assumption is in line 1 and the conclusion or goal is in line 6. The proof checker starts off by writing the assumption for me. You would simply state it on line 1 if you are not using a proof checker. In the reference section is the link to the proof checker that I am using. You may use as well for future exercises as a way to check if your proofs are correct.

Since the premise is a disjunction (an "or" proposition), I need to consider two cases. The first case, "B", I considered in lines 2 and 3. The second case, "A", I considered in lines 4 and 5. I need to get the same result in both cases to invoke the disjunction elimination (∨E) rule, which I did on line 6. Note that I had to use the disjunction introduction (∨I) rule on lines 3 and 5. Since it did not matter which order I used I used the order I needed for the goal.

You may be required to use other rules or other names for the rules than the ones I used.

---

References

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

share|improve this answer

share|improve this answer

answered 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Frank Hubeny

4,4153938

4,4153938

add a comment | 

add a comment | 

up vote
2
down vote

Let's discuss the intuitive meaning of B∨A. It means either B or A.

If that is the case then, writing any disjunct first or last should not truth functionally matter.

Now, let's go to the truth table:

B A (B∨A) (A∨B) 
T T T T
T F T T
F T T T
F F F F

As you can see the corresponding truth values are identical and therefore, (A∨B)≡(B∨A).

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
  – Frank Hubeny
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @FrankHubeny Thank you for the edit, That is precisely how I wanted it.
  – Bertrand Wittgenstein's Ghost
  3 hours ago
  

  
  
  
  

add a comment | 

up vote
2
down vote

Let's discuss the intuitive meaning of B∨A. It means either B or A.

If that is the case then, writing any disjunct first or last should not truth functionally matter.

Now, let's go to the truth table:

B A (B∨A) (A∨B) 
T T T T
T F T T
F T T T
F F F F

As you can see the corresponding truth values are identical and therefore, (A∨B)≡(B∨A).

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
  – Frank Hubeny
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @FrankHubeny Thank you for the edit, That is precisely how I wanted it.
  – Bertrand Wittgenstein's Ghost
  3 hours ago
  

  
  
  
  

add a comment | 

up vote
2
down vote

up vote
2
down vote

Let's discuss the intuitive meaning of B∨A. It means either B or A.

If that is the case then, writing any disjunct first or last should not truth functionally matter.

Now, let's go to the truth table:

B A (B∨A) (A∨B) 
T T T T
T F T T
F T T T
F F F F

As you can see the corresponding truth values are identical and therefore, (A∨B)≡(B∨A).

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

Let's discuss the intuitive meaning of B∨A. It means either B or A.

If that is the case then, writing any disjunct first or last should not truth functionally matter.

Now, let's go to the truth table:

B A (B∨A) (A∨B) 
T T T T
T F T T
F T T T
F F F F

As you can see the corresponding truth values are identical and therefore, (A∨B)≡(B∨A).

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this answer

share|improve this answer

edited 4 hours ago

Frank Hubeny

4,4153938

edited 4 hours ago

Frank Hubeny

4,4153938

edited 4 hours ago

Frank Hubeny

4,4153938

4,4153938

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

answered 4 hours ago

Bertrand Wittgenstein's Ghost

414

414

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

New contributor

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

Bertrand Wittgenstein's Ghost is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
  – Frank Hubeny
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @FrankHubeny Thank you for the edit, That is precisely how I wanted it.
  – Bertrand Wittgenstein's Ghost
  3 hours ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
  – Frank Hubeny
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @FrankHubeny Thank you for the edit, That is precisely how I wanted it.
  – Bertrand Wittgenstein's Ghost
  3 hours ago
  

  
  
  
  

I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
– Frank Hubeny
4 hours ago

I made an edit which you may roll back or continue editing. I hope I got the formatting as you intended it. Welcome to this SE!
– Frank Hubeny
4 hours ago

@FrankHubeny Thank you for the edit, That is precisely how I wanted it.
– Bertrand Wittgenstein's Ghost
3 hours ago

@FrankHubeny Thank you for the edit, That is precisely how I wanted it.
– Bertrand Wittgenstein's Ghost
3 hours ago

add a comment | 

MoIsStillHere is a new contributor. Be nice, and check out our Code of Conduct.

 

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