and or conditional reversal Forum

[Br3v]

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]

In other words if we have

x and y > z

Can this exist?

Not z > not x and not y

[lovejopd]

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]

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]

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]

Brev,

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


http://www.top-law-schools.com/forums/v ... 6&t=180664

HTH.

[Easy-E]

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.