and or conditional reversal

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Br3v

Posts: 4272
Joined: Mon Jun 13, 2011 7:18 pm

and or conditional reversal

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?

Br3v

Posts: 4272
Joined: Mon Jun 13, 2011 7:18 pm

Re: and or conditional reversal

In other words if we have

x and y > z

Can this exist?

Not z > not x and not y

lovejopd

Posts: 544
Joined: Tue Dec 01, 2009 1:00 pm

Re: and or conditional reversal

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!

Br3v

Posts: 4272
Joined: Mon Jun 13, 2011 7:18 pm

Re: and or conditional reversal

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: 2878
Joined: Mon May 09, 2011 11:34 pm

Re: and or conditional reversal

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.

Geetar Man

Posts: 564
Joined: Wed May 26, 2010 4:13 am

Re: and or conditional reversal

Brev,

viewtopic.php?f=6&t=180664

HTH.

Easy-E

Posts: 6487
Joined: Fri Feb 18, 2011 1:46 pm

Re: and or conditional reversal

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.