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Diagramming Practice – School Dance

Diagram the following conditional statement and any valid inferences it implies: “Arnold will go with Shaina to the dance if, and only if, she thinks he is cute.”


The diagramming keyword here is “if, and only if.”  This phrase is a bit weird in that it indicates a condition that is both sufficient and necessary.  So, we can really put either term of this statement on either side of the arrow.  And, we can throw in a double-sided arrow this time because the relationship goes in both directions—that is, both terms are sufficient conditions and both terms are necessary conditions.  Also, notice that there are four valid inferences to draw from this statement.

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