# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 25 May 2013 03:20:03 UTC

 All times are UTC [ DST ]

 Page 1 of 2 [ 22 posts ] Go to page 1, 2  Next
 Print view Previous topic | Next topic
Author Message
 Post subject: proof analysisPosted: Sun, 30 Jan 2011 16:35:26 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

Top

 Post subject: Re: proof analysisPosted: Sun, 30 Jan 2011 16:36:53 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 02:10:35 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 02:48:36 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:00:42 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

Because :

Since b>1 and 1>0 ,then b>0 and thus ab>2b

Also 2>0 hence 2b>2

So ab>2b and 2b>2,implying that ab>2

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:03:23 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

Because :

Since b>1 and 1>0 ,then b>0 and thus ab>2b

Also 2>0 hence 2b>2

So ab>2b and 2b>2,implying that ab>2

Right, now if you can just put names to those reasons--eg. the last one a>b and b>c implies a>c is called the transitive property--you will have the answer to the rest of the problem.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:15:10 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

Because :

Since b>1 and 1>0 ,then b>0 and thus ab>2b

Also 2>0 hence 2b>2

So ab>2b and 2b>2,implying that ab>2

Right, now if you can just put names to those reasons--eg. the last one a>b and b>c implies a>c is called the transitive property--you will have the answer to the rest of the problem.

How about the laws of logic ??

Surely the transitive property is not a law of logic

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:19:39 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
idi wrote:
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

Because :

Since b>1 and 1>0 ,then b>0 and thus ab>2b

Also 2>0 hence 2b>2

So ab>2b and 2b>2,implying that ab>2

Right, now if you can just put names to those reasons--eg. the last one a>b and b>c implies a>c is called the transitive property--you will have the answer to the rest of the problem.

How about the laws of logic ??

Surely the transitive property is not a law of logic

Most everything there is Modus Tollens or Modus Ponens.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:22:57 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
idi wrote:
idi wrote:
idi wrote:
1) Prove that: if a>2 and b>1 ,then ab>2

2)State rhe axioms ,theorems or the definitions involved int he proof

3) State the laws of logic involved in the proof

What have you tried?

Only the proof:

(a>2 and b>1) => (ab>2b and 2b>2) => ab>2

Okay, how do you know it's legal to do that?

Because :

Since b>1 and 1>0 ,then b>0 and thus ab>2b

Also 2>0 hence 2b>2

So ab>2b and 2b>2,implying that ab>2

Right, now if you can just put names to those reasons--eg. the last one a>b and b>c implies a>c is called the transitive property--you will have the answer to the rest of the problem.

How about the laws of logic ??

Surely the transitive property is not a law of logic

Most everything there is Modus Tollens or Modus Ponens.

How and where ??

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 03:24:12 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
How and where ??

If you cannot follow your own logic, then there's more of a problem than an analysis. Try and spot what you're doing, it's good to learn how you think.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 14:19:37 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
How and where ??

If you cannot follow your own logic, then there's more of a problem than an analysis. Try and spot what you're doing, it's good to learn how you think.

How can one follow his own logic ?

Can you give an example??

How can somebody learn how to think??

Can you again give an example??

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 14:54:48 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
idi wrote:
How and where ??

If you cannot follow your own logic, then there's more of a problem than an analysis. Try and spot what you're doing, it's good to learn how you think.

How can one follow his own logic ?

Can you give an example??

How can somebody learn how to think??

Can you again give an example??

I mean if I look at how I reason it's simple.

Code:
If A is a field, A is also a ring.

B is a field, hence B is a ring.

It's easy to see this is modus ponens.

So just look at each step, write out in words what your reasoning is. If you need to, you can also make a list of the logical inference rules then compare the forms of your reasoning sentences with the list and decide which rule you are using.

As for how someone can learn to think, that's a mystery even to the best psychologists. I recommend just reading a lot of proofs and getting used to how they read, and trying to write some yourself to mimic those. In this way you get practice learning what "good thinking" is like and attempting to duplicate it.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 21:27:05 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53
idi wrote:
idi wrote:
How and where ??

If you cannot follow your own logic, then there's more of a problem than an analysis. Try and spot what you're doing, it's good to learn how you think.

How can one follow his own logic ?

Can you give an example??

How can somebody learn how to think??

Can you again give an example??

I mean if I look at how I reason it's simple.

Code:
If A is a field, A is also a ring.

B is a field, hence B is a ring.

It's easy to see this is modus ponens.

This is not Modus Ponens

The general form of Modus Ponenes is:

[(p=>q) and p] => q

Is the above of that form??

Quote:
So just look at each step, write out in words what your reasoning is. If you need to, you can also make a list of the logical inference rules then compare the forms of your reasoning sentences with the list and decide which rule you are using.

As for how someone can learn to think, that's a mystery even to the best psychologists. I recommend just reading a lot of proofs and getting used to how they read, and trying to write some yourself to mimic those. In this way you get practice learning what "good thinking" is like and attempting to duplicate it.

honestly i make nothing out of the above

Top

 Post subject: Re: proof analysisPosted: Mon, 31 Jan 2011 22:49:52 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
idi wrote:
idi wrote:
idi wrote:
How and where ??

If you cannot follow your own logic, then there's more of a problem than an analysis. Try and spot what you're doing, it's good to learn how you think.

How can one follow his own logic ?

Can you give an example??

How can somebody learn how to think??

Can you again give an example??

I mean if I look at how I reason it's simple.

Code:
If A is a field, A is also a ring.

B is a field, hence B is a ring.

It's easy to see this is modus ponens.

This is not Modus Ponens

The general form of Modus Ponenes is:

[(p=>q) and p] => q

Is the above of that form??

honestly i make nothing out of the above

This IS Modus Ponens. If you cannot recognize it, then you need some more practice with that. P is the statement (A is a field) Q is the statement (A is a ring).

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: proof analysisPosted: Tue, 1 Feb 2011 01:34:54 UTC
 Senior Member

Joined: Fri, 28 May 2010 02:57:26 UTC
Posts: 53

Code:
If A is a field, A is also a ring.

B is a field, hence B is a ring.

It's easy to see this is modus ponens.

.

idi wrote:

This is not Modus Ponens

The general form of Modus Ponenes is:

[(p=>q) and p] => q

Is the above of that form
??

This IS Modus Ponens. If you cannot recognize it, then you need some more practice with that. P is the statement (A is a field) Q is the statement (A is a ring).

If you put :

P = (A is a field) ...........Q = ( A is a ring).

Can we put then : P=(B is a field) and CONCLUDE ,(B is a ring) is a Q,by using M.Ponenes ??

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 2 [ 22 posts ] Go to page 1, 2  Next

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous