# What does "A or B does not..." mean?

In a digital card game I'm playing I see this text:

`If this follower's attack or defense has not been increased by a spell or effect, destroy this follower.` ("attack" and "defense" is a numeric value of this follower.)

I'm confused about the segment of `If attack or defense has not been increased`. Does this mean:

1. "`attack has not been increased` or `defense has not been increased`", or

2. "`attack has not been increased` and `defense has not been increased`", since due to De Morgan's laws `NOT (A or B) = (NOT A) and (NOT B)`?

Thank you.

• To some extent your guess is as good as anyone else's will be. My personal feeling is that it's `~ (A ∨ B)`, which is to say, if either is true then don't destroy. Aug 20, 2019 at 4:36
• I read it as option 2. Aug 20, 2019 at 6:25
• I agree with both previous comments (which essentially say the same thing) but would like to suggest that "If neither the attack nor defence of this follower has been increased..." would have been clearer" Aug 20, 2019 at 7:23

Although I think the sentence is not entirely unambiguous, I reckon that in colloquial language, too, the second interpretation would be favoured.

Take this colloquial example: 'if you haven't eaten the chocolate or the cake, you can have the pie'. It implies that you can have the pie only if you have eaten neither cake nor chocolate.

That is opposed to 'if you haven't eaten the chocolate and the cake, you can have the pie', which implies you can have the pie unless you have eaten both chocolate and cake.

• This answer looks good to me, why is it downvoted? Aug 22, 2019 at 5:59

I assume the situation is that one of the players had in hand a card to be used at any time when it is tactically possible. Presumably, also, there are cards that allow the holder to make an attack and others that can be played in defense. It appears that if you hold this card, and are making an attack, you can use it to destroy a ‘defender’ played to ward off your attack. If you are being attacked, then you can play this card to successfully destroy the ‘attack’ card. It is surely something like that. But they have to fit the sentence onto the card itself and so cannot write all that.

Disjunctions (‘or’) are problematic. This is because ‘or’ itself is ambiguous.

1. The inclusive or: as in “Would you like milk or sugar in your tea?”. This clear asks if you want milk or sugar or both. The answer “Yes please” would be inept, and probably get you a spoon of sugar and a splash of milk, even if you only wanted the milk and hate sugary tea.

2. The exclusive or: as in “Should I put petrol or diesel in your tank?”. Anyone who knows about cars knows that this has to mean one or the other but not both!!

The truth conditions for these two meanings are easy to state.

1.Inclusive Disjunction. Where A and B stand for statements, the proposition “A or B” is true if and only if the statement “A and B are (both) false.” is untrue. in other words, one or both must be true.

1. Exclusive Disjunction. In this case “A or B” is true if and only if one or the other (but not both) is true.

In the context of your game, the holder of this ‘override’ card cannot be attacking and defending at the same time. Nor can the player against whom s/he uses the card be attacking and defending at the same time. Similarly, you can only use this card against an attacker if you are defending against them. And you can only use it against a defender if you are attacking them.

They are, in effect alternatives.

• I'm sorry not to mention, but here `attack` means "value of attack (power)" and `defense` means its "life point". Aug 22, 2019 at 5:49
• @RomulusUrakagiTs'ai What you say illustrates the importance of explaining the full context that lies behind your question. Aug 22, 2019 at 5:55
• Very true. Also, I'm unsure about applying De Morgan's laws since `attack` (and `defense`) is not a statement but an object, so itself can't be true or false. Aug 22, 2019 at 5:57