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Diagramming Practice – Cakes

Diagram the following conditional statement and find its contrapositive: “The cakes are delicious, except for the gluten-free ones.”


To diagram a statement involving the word “except,” you should first change the word “except” to the phrase “if not.”  Then, you can diagram the resulting sentence as an “if” statement.  So, the sufficient condition becomes “NOT gluten-free.”  The necessary condition is “delicious.”  If you wanted to get really specific, the sufficient condition would technically be “cake AND not gluten-free.”  This is because we are not talking about everything that is not gluten-free, but rather just cakes that are not gluten-free.  Whether or not you needed to be this specific would depend on the context of the specific question in which this statement appeared.

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