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I'm trying to make more sense of how negation effects how a sentence is parsed and understood if and's and or's are used within them.

Pop quiz: You are trapped on a bus with a bomb going 50 MPH. You have a radio... (okay enough Keanu Reeves references) :-)

Let's say the bomb expert says "Don't cut the red or green wires." I think that means "Do not cut the wires colored red. Do not cut the wires colored green."

Now, let's say the bomb expert said on the radio "Do not cut the red and green wires", instead. Do I take that to mean:

"Do not cut the wires colored red. Do not cut the wires colored green."

OR

"Do not cut the wires whose insulation has red and green stripes." ?

OR

"It's okay to cut the wires colored red or the wires colored green, as long I don't cut one of each color."

Which meaning should I take if the radio breaks and I can't ask follow up questions?

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In English, it's ambiguous. (Formal logic is a different issue entirely.) –  Kosmonaut May 21 '11 at 20:31

2 Answers 2

up vote 2 down vote accepted

Don't cut the red or green wires.

"The initial negative carries through to all the enumerated elements”, so this is the same as saying "Don't cut the red wires. Don't cut the green wires".

"Do not cut the red and green wires"

This depends on context. It cannot be the same as the former, so it must either refer to wires colored both red and green – or to the combination of individual red and green wires.

You might get a hint from the enunciation – if the wire is red-green, it will often be spoken quickly "redandgreen wires" (to match the written version, which has the primary color first and the stripe color second). Then again, it's likely that you're in a panic – so everything sounded fast.

Which meaning should I take if the radio breaks and I can't ask follow up questions?

Well, first – curse the expert for not just telling you which wire to cut. After that, it depends on what wires you see. In increasing order of blowing up, I'd do the following:

Assuming red wire with green stripe (red-green), red wire, green wire, other wires:

  1. Cut the other wires. These are clearly not prohibited.
  2. Cut one of the red or green wires. These were either not prohibited at all (if the expert meant red-green), or not prohibited individually.
  3. Cut the red-green wire. You're really taking a chance here – but unless there was some clear indication (such as a dropped or very fast "and"), I'd assume the expert would have spoken "redgreen" or "red with green stripe" to call out this wire.
  4. The only thing left is the remaining red or green wire. You've probably blown up by now.
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The meaning is ambiguous, so it's very difficult to tell. Also remember that it depends on the person making the statement, especially whether the person is a logical thinker, or not.

As a programmer/coder, I can tell you how it works in terms of pure logic.

First we must resolve the ambiguity problem, so there are 2 options of what the person might be stating:

Option A: Do not cut the (red and green) wires.

This is obvious. There is a group of wires consisting of at least 2 wires coloured "red and green". This type of wires you cannot cut.

Option B: Do not cut the ((red) and (green) wires).

Here we have 2 types of wires being talked about: red and green. You are being told not to cut them. The statements are connected with and, that means both brackets must "be true".

Therefore: You will properly obey this command if and only if both the wires (red and green) remain uncut, therefore you cannot cut either.

If the person says:

Do not cut the ((red) or (green) wires).

Then logically, at least one of those statements must be true for the whole statement to be true, so to obey this command, you have to cut at least 1 wire and you may not cut the other. Logically, it doesn't matter which you choose to cut and which you choose not to.

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