Diagramming Key Words Conditional Logic Overview Conditional statements are essentially "If-then" statements. They are hypothetical relationships that aren't absolutely true, but instead are reliant on some condition being true. ● “If Jim takes the bridge he’ll be late to work” — Conditional statement ● “Jim is late to work” — Absolute statement (not conditional) Two conditions make up a conditional statement: the Sufficient condition, and the Necessary condition. ● Sufficient condition — The "if" side of the condition, aka the thing that is sufficient to guarantee the other side. ● Necessary condition — The "then" side of the condition, aka the thing that is required for the sufficient condition to be true. Always diagram using an arrow: Sufficient condition of the left, Necessary condition on the right. Contrapositive — A logically equivalent form of a conditional statement. Every conditional statement has one. A conditional and its contrapositive mean the same thing, but displaying it in this other way can often be helpful. 1. Start with original condition 2. Flip the necessary and sufficient conditions 3. Negate the conditions (positive becomes negative and vice versa) KEY WORDS — aka How To Identify Conditional Statements 1. Sufficient key words — Words that indicate "enough" ● All, Every, Any, Each, Whenever, Anyone ● E.g., "Every Student takes math at this school." ○ Student → Math 2. Necessary key words — Words that indicate "requirement" ● Only, Only if, Needs, Must, Requires, Prerequisite ● E.g., "Taking philosophy 101 is a requirement for graduating with a philosophy degree." ○ Graduating → Philosophy 101 3. "If not" words — Easiest way to diagram statements with these words is to cross off the word when we see it and replace it with "if not." ● Unless, Until, Except, Without ● E.g., "The party will be fun unless Bob arrives." ○ "The party will be fun unless IF NOT Bob arrives." ○ ~Bob → Fun ■ Contrapositive: ~Fun → Bob 4. "No torpedo" — In statements phrased as "No A's are B's," the necessary condition is actually the one that's being negated, even though the "no" comes right before the sufficient. You can also think of it as translating to "ALL A's are NOT B's." ● No, None, Nothing, Nobody ○ Use when one of these words starts a sentence AND there's no other good conditional indicator ● E.g., "No dogs are cats." ○ Dog → ~Cat ● E.g., None of the classes in the business program adequately prepare you for life in the corporate world ○ Business class → ~prepared Fallback — If you find yourself struggling on how to diagram it can be helpful to go back to the basics. What’s needed to be true? Which of these terms would guarantee the other would be true? ● Also, rephrasing the statement into "if-then" form can be a helpful stepping-stone to diagramming the statement correctly.
