The only preexisting recordings that are transferred onto compact disc are those that record companies believe will s...

CassGabriel on March 8, 2020

Im confused

we have been taught for the "no" a's are B to diagram A - Not B. How can we just all the sudden disregard this rule and treat is at no a- no b? How am I going to know when to use this exemption on the rule?

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Skylar on March 8, 2020

@CassGabriel, happy to help!

There is no exception to the rule, and we are not disregarding it here. Rather than a "No A's are B's" setup here, we have a "No NOT A's are B's" setup.

You are correct that we can diagram "No A's are B's" as: A -> NOT B. The contrapositive of this is B -> NOT A.

However, answer choice (E) states that "NO recording that is NOT played on the radio is one that record companies believe would be profitable if transferred to compact disc." This is a deviation from the "No A's are B's" logic we diagrammed above because we are dealing with "NOT A's" instead of "A's."

Here, A = PR (played on the radio) and B = BP (believed to be profitable).

We can start to diagram (E) by following our original "No A's are B's" diagram to get: A -> NOT B. However, since instead of "A" here we have "NOT A", we need to negate A. This gives us: NOT A -> NOT B. In the terms of the real variables, this is: NOT PR -> NOT BP. The contrapositive of this is BP -> PR.

Does that make sense? Please let us know if you have any other questions and best of luck with your studies!