How to prove the following statement? [closed]

Clash Royale CLAN TAG#URR8PPP

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a=b ∨ a=c ∨ b=c = T

I have expanded the LHS as follows. But have no clue how to continue from there

(a=>b)∧(b=>a) ∨ (a=>c)∧(c=>a) ∨ (b=>c)∧(c=>b)

Link for the question [Q (p)].
http://www.cs.utoronto.ca/~hehner/aPToP/solutions/Ex6.pdf

The solution is not understood.

formal-proofs

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asked Jul 29 at 2:47

Dhananjaya Senanayake

6

closed as off-topic by Shailesh, Leucippus, Lord Shark the Unknown, TheGeekGreek, John Ma Jul 29 at 8:44

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Leucippus, TheGeekGreek

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
  – Aniruddha Deshmukh
  Jul 29 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
  – Dhananjaya Senanayake
  Jul 29 at 4:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
  – Taroccoesbrocco
  Jul 29 at 4:11
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
  – Dhananjaya Senanayake
  Jul 29 at 4:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
  – Aniruddha Deshmukh
  Jul 29 at 4:23
  

  
  
  
  

 | 
show 8 more comments

up vote
0
down vote

favorite

a=b ∨ a=c ∨ b=c = T

I have expanded the LHS as follows. But have no clue how to continue from there

(a=>b)∧(b=>a) ∨ (a=>c)∧(c=>a) ∨ (b=>c)∧(c=>b)

Link for the question [Q (p)].
http://www.cs.utoronto.ca/~hehner/aPToP/solutions/Ex6.pdf

The solution is not understood.

formal-proofs

share|cite|improve this question

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

closed as off-topic by Shailesh, Leucippus, Lord Shark the Unknown, TheGeekGreek, John Ma Jul 29 at 8:44

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Leucippus, TheGeekGreek

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
  – Aniruddha Deshmukh
  Jul 29 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
  – Dhananjaya Senanayake
  Jul 29 at 4:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
  – Taroccoesbrocco
  Jul 29 at 4:11
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
  – Dhananjaya Senanayake
  Jul 29 at 4:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
  – Aniruddha Deshmukh
  Jul 29 at 4:23
  

  
  
  
  

 | 
show 8 more comments

up vote
0
down vote

favorite

up vote
0
down vote

favorite

a=b ∨ a=c ∨ b=c = T

I have expanded the LHS as follows. But have no clue how to continue from there

(a=>b)∧(b=>a) ∨ (a=>c)∧(c=>a) ∨ (b=>c)∧(c=>b)

Link for the question [Q (p)].
http://www.cs.utoronto.ca/~hehner/aPToP/solutions/Ex6.pdf

The solution is not understood.

formal-proofs

share|cite|improve this question

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

a=b ∨ a=c ∨ b=c = T

I have expanded the LHS as follows. But have no clue how to continue from there

(a=>b)∧(b=>a) ∨ (a=>c)∧(c=>a) ∨ (b=>c)∧(c=>b)

Link for the question [Q (p)].
http://www.cs.utoronto.ca/~hehner/aPToP/solutions/Ex6.pdf

The solution is not understood.

formal-proofs

share|cite|improve this question

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

share|cite|improve this question

share|cite|improve this question

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

asked Jul 29 at 2:47

Dhananjaya Senanayake

6

6

closed as off-topic by Shailesh, Leucippus, Lord Shark the Unknown, TheGeekGreek, John Ma Jul 29 at 8:44

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Leucippus, TheGeekGreek

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Shailesh, Leucippus, Lord Shark the Unknown, TheGeekGreek, John Ma Jul 29 at 8:44

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Leucippus, TheGeekGreek

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
  – Aniruddha Deshmukh
  Jul 29 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
  – Dhananjaya Senanayake
  Jul 29 at 4:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
  – Taroccoesbrocco
  Jul 29 at 4:11
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
  – Dhananjaya Senanayake
  Jul 29 at 4:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
  – Aniruddha Deshmukh
  Jul 29 at 4:23
  

  
  
  
  

 | 
show 8 more comments

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
  – Aniruddha Deshmukh
  Jul 29 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
  – Dhananjaya Senanayake
  Jul 29 at 4:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
  – Taroccoesbrocco
  Jul 29 at 4:11
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
  – Dhananjaya Senanayake
  Jul 29 at 4:23
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
  – Aniruddha Deshmukh
  Jul 29 at 4:23
  

  
  
  
  

1

1

Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
– Aniruddha Deshmukh
Jul 29 at 3:48

Could you give more background about the questions? I am not understanding what we are proving and why we are doing so!
– Aniruddha Deshmukh
Jul 29 at 3:48

@AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
– Dhananjaya Senanayake
Jul 29 at 4:04

@AniruddhaDeshmukh will you follow the link provided. It has similar proof questions like this.
– Dhananjaya Senanayake
Jul 29 at 4:04

Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
– Taroccoesbrocco
Jul 29 at 4:11

Please, instead of posting links, could you type some words in order to explain what you are talking about? If $a$, $b$ and $c$ represent propositions, what is the meaning of $a = b$? What is T?
– Taroccoesbrocco
Jul 29 at 4:11

@Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
– Dhananjaya Senanayake
Jul 29 at 4:23

@Taroccoesbrocco, a=b means if and only if, a=>b means if then, and T means binary Truth or 1 .
– Dhananjaya Senanayake
Jul 29 at 4:23

@DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
– Aniruddha Deshmukh
Jul 29 at 4:23

@DhananjayaSenanayake It does have the proof. But, I am not getting the context. Why is it so? What are $a, b, c$? Kindly clarify!
– Aniruddha Deshmukh
Jul 29 at 4:23

 | 
show 8 more comments

1 Answer
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1
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Lets say without loss of generality that $a<=>b$. Then, a and b are both true or both false, which means that $a=>b$ and $b=>a$.

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

Lets say without loss of generality that $a<=>b$. Then, a and b are both true or both false, which means that $a=>b$ and $b=>a$.

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

add a comment | 

up vote
1
down vote

Lets say without loss of generality that $a<=>b$. Then, a and b are both true or both false, which means that $a=>b$ and $b=>a$.

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

add a comment | 

up vote
1
down vote

up vote
1
down vote

Lets say without loss of generality that $a<=>b$. Then, a and b are both true or both false, which means that $a=>b$ and $b=>a$.

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

Lets say without loss of generality that $a<=>b$. Then, a and b are both true or both false, which means that $a=>b$ and $b=>a$.

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

share|cite|improve this answer

share|cite|improve this answer

answered Jul 29 at 6:41

Eulerrr

1646

answered Jul 29 at 6:41

Eulerrr

1646

answered Jul 29 at 6:41

Eulerrr

1646

1646

add a comment | 

add a comment |