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Question about example on p. 73 of LGB (unless/until)

lsat_novice
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The following example is on page 73 of the Logic Games Bible:

"G cannot be cleaned until F is cleaned, unless F is cleaned second."

The book says that this can be diagrammed in the following way: (G -- F) --> F2 (imagine the 2 is a subscript).

I'm confused by this because:

Step 1: "G cannot be cleaned until F is cleaned" ... this contains "until" so I thought that this part of the sentence would be diagrammed G -- F. ("Until" negates the sufficient condition.)

Step 2: "Unless F is cleaned second." Because of "unless," I thought that this should negate the first part of the sentence. So I thought that (G -- F) should be turned into a negative. But the book doesn't do this... it keeps (G -- F) as it is in Step 1.

Can someone please explain?
Thank you!
Jonathan Evans
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Hi!

Good question!

Here the "until" refers to the order of the variables G and F. This "until" is not part of the conditional structure.

Think of it like this:

    "G is cleaned after F unless F is cleaned second."

Notice that in the way that I phrased the rule above I have omitted the "until" without changing the meaning of the sentence, and the Unless Equation™ still works correctly:

  1. Negate the sufficient condition: (F :longline: G) becomes (G :longline: F)
  2. Keep the necessary condition intact: F2
  3. (G :longline: F) :arrow: F2

Conditional statements such as these are sometimes difficult to parse. In situations such as these, it helps to separate out the conditions and the conditional language that dictates what we do with them. Look at the example statement separated out thus:

    "G cannot be cleaned until F is cleaned" UNLESS "F is cleaned second"

The statements in the quotation marks above are the two conditions. The "unless" tells us what to do with them. Use the "unless" to determine which statement is sufficient and which is necessary. Then negate as needed according to the Unless Equation.

Does this make sense? Please follow up with further questions.
lsat_novice
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Posts: 30
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Thanks so much for the detailed (and prompt!) explanation, Jonathan!