and or conditional reversal

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Br3v
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and or conditional reversal

Postby Br3v » Tue Mar 20, 2012 9:02 pm

If x and y > z

Reversal of this would be:

If not z > not x or not y

Correct?

Now, could it be true that not z allows for both not x and not y? Or does not z only mean not x or not y but both not x and not y is impossible?

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Br3v
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Re: and or conditional reversal

Postby Br3v » Tue Mar 20, 2012 9:03 pm

In other words if we have

x and y > z

Can this exist?

Not z > not x and not y

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lovejopd
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Re: and or conditional reversal

Postby lovejopd » Tue Mar 20, 2012 9:08 pm

Yes, generally "or" is inclusive, which include "both" unless it is stated 'not both' in Game

1. A or B can mean 3 things
1. Only A(O)
2. Only B(O)
3. A and B(O)
NOT
4. nothing (X)

2. A or B(but not both) mean 2 things
1. Only A(O)
2. Only B(O)
NOT
3. A and B (X)
4. Nothing (X)
1. A --> B or C
~B AND ~C --> ~A

2. A --> B and C
~B or ~C --> ~A

Simply pay attention to the transition from OR to AND or vice versa when doing contrapositive

Hope this helps!

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Br3v
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Re: and or conditional reversal

Postby Br3v » Tue Mar 20, 2012 9:11 pm

lovejopd wrote:Yes, generally "or" is inclusive, which include "both" unless it is stated 'not both' in Game

1. A or B can mean 3 things
1. Only A(O)
2. Only B(O)
3. A and B(O)
NOT
4. nothing (X)

2. A or B(but not both) mean 2 things
1. Only A(O)
2. Only B(O)
NOT
3. A and B (X)
4. Nothing (X)
1. A --> B or C
~B AND ~C --> ~A

2. A --> B and C
~B or ~C --> ~A

Simply pay attention to the transition from OR to AND or vice verse when doing contrapositive

Hope this helps!


It did thanks

kaiser
Posts: 2940
Joined: Mon May 09, 2011 11:34 pm

Re: and or conditional reversal

Postby kaiser » Tue Mar 20, 2012 9:13 pm

Unless told otherwise, the word "or" doesn't mean just one or the other in a mutually exclusive way

X and Y --> Z

Not Z --> Not X or Not Y (or both)

Whenever you write "or", you can just think of it as having the term "or both" at the end. If you have neither X nor Y, then of course the term "not X or not Y" is satisfied.

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Geetar Man
Posts: 585
Joined: Wed May 26, 2010 4:13 am

Re: and or conditional reversal

Postby Geetar Man » Tue Mar 20, 2012 9:31 pm

Brev,

Here is a thread I made that is relevant to your question.


viewtopic.php?f=6&t=180664

HTH.

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Easy-E
Posts: 5690
Joined: Fri Feb 18, 2011 1:46 pm

Re: and or conditional reversal

Postby Easy-E » Wed Mar 21, 2012 9:39 am

kaiser wrote:Unless told otherwise, the word "or" doesn't mean just one or the other in a mutually exclusive way

X and Y --> Z

Not Z --> Not X or Not Y (or both)

Whenever you write "or", you can just think of it as having the term "or both" at the end. If you have neither X nor Y, then of course the term "not X or not Y" is satisfied.



Yepp, unless explicitly state, "or" is inclusive. Basically what you can take away from the contrapositive of kaiser's example is that if you don't have Z, then you cannot have both X and Y occurring, but one of the two could. That was probably redundant, but HTH.




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