We recently received the following question from a student:
"For question 11, I think the answer should be (F  G) > F2, since the question says G cannot be cleaned UNTIL F is cleaned, unless F is cleaned second."
LGB 2018 edition p. 73
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Hi!
Good question! First, there's not an error, but this is a tricky statement so let's look at it more closely. Start by using the Unless Equation™:
Let's use the equation here:
1. "F cleaned second" becomes the necessary condition.
2. "G cannot be cleaned until F is cleaned." First, diagram this.
Now, negate it.
This becomes the sufficient condition. This is how we get:
Let's discuss briefly what this statement means to reiterate how and why the Unless Equation works.
What does this mean? Our baseline scenario is one in which "G cannot be cleaned until F is cleaned" (F G). This is the way is has to be always, except for one scenario. In the event F is cleaned second (F2), then it is possible to have G before F. Thus, what do we know? In all the scenarios in which F is not second, G is coming after F. This idea can be represented as follows:
Notice that this is the contrapositive of the conditional statement we made above using the Unless Equation:
Remember that a conditional and its contrapositive are logically equivalent. Therefore, the explanation in the book is correct. I hope this helps!
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