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I understand the basics of conditional logic however I get tripped up when I try to translate some sentences into diagrams. Can someone please help me with the following?

1) If A then and only then B. Is this A->B or A<->B?

2) This one is from PT45, Sec 4, #18: "Divisions of a large institution functioning autonomously always permits realistic planning." I translated this as (autonomous) -> (realistic planning). This question asks which of the answer choices are most strongly supported by the above. The correct answer is ~(autonomous) -> ~(maximally realistic). I didn't choose this answer because this can't be inferred from the translation I made (auto) -> (realistic).

3) PT45, Sec4, #22
I got totally confused on this one. This is a logically if assumed.
"The only recordings that are transferred are those that will sell". I translated this (recordings that are transferred) -> (will sell). "Most jazz not transferred because few jazz played on radio". How do I diagram this sentence? Also the answer is E.

Thanks a lot!

1. A <-> B

2. I don't have PT 45, but the sentence you quoted would be translated as (realistic planning) -> (autonomous), so the answer is just the contrapositive of that. The word "permits" is a little confusing-- just because the divisions are functioning autonomously doesn't guarantee that they will have realistic planning (which is what your translation implies). "Functioning autonomously" is the necessary condition which permits "realistic planning," the sufficient condition.

3. I'm not sure about your question, since I don't have PT 45

Hope this can help you somewhat!

skippy1 wrote:2) This one is from PT45, Sec 4, #18: "Divisions of a large institution functioning autonomously always permits realistic planning." I translated this as (autonomous) -> (realistic planning). This question asks which of the answer choices are most strongly supported by the above. The correct answer is ~(autonomous) -> ~(maximally realistic). I didn't choose this answer because this can't be inferred from the translation I made (auto) -> (realistic).

The quote you gave isn't actually what the stimulus says, and the difference crucial to the answer. The real line is: "Decentralization enables divisions of a large institution to function autonomously. This always permits more realistic planning". The key to that sentence is that autonomy always permits *more* realistic planning than non-autonomy. So, maximally realistic planning will always include autonomy, otherwise whatever level of planning attained could be improved upon with autonomy. Kind of an unusual stimulus.

Thanks a lot!