A Universal-Particular (U-P) argument Test the validity of this argument: All cats have rodent breath. Whiskers doesn't have rodent breath. Thus, Whiskers isn't a cat. A. Valid B. Invalid This is an example of a Universal-Particular argument -- that is, an argument in in which one premise is a universal statement and the other premise and conclusion are statements about a particular individual.

Solution Test the validity of this argument: All cats have rodent breath. Whiskers doesn't have rodent breath. Thus, Whiskers isn't a cat. This argument is valid, because, as we shall explain in the next few slides, it can be reduced to the form Contrapositive Reasoning.

A Universal-Particular (U-P) argument All cats have rodent breath. Whiskers doesn't have rodent breath. Thus, Whiskers isn't a cat. A universal statement is a categorical statement of the form “all are…” or “none are…”, such as “All cats have rodent breath” or “No elephants are tiny.” A universal statement describes a general relationship between two categories. A particular statement describes the relationship between an individual and a category. “Whiskers isn’t a cat” is an example of a particular statement. “Dumbo is an elephant” is another particular statement.

Universal statements Statements of the form “All are…” or “None are…” are called universal statements. These can be informally turned into conditional statements. For instance, the statement “All cats have rodent breath” can be informally re-phrased as “If one is a cat, then one has rodent breath,” or “If ___ is a cat, then ___ has rodent breath.” “All cats have rodent breath” is an example of a universal positive statement.

Negative universal statements A statement of the form “none are…” is called a universal negative statement. Negative universal statements can also be re-phrased as conditional statements. For instance “No cats are dogs” can be informally re-phrased as “If one is a cat, then one is not a dog,” or “If ___ is a cat, then ___ is not a dog.”

Another U-P argument No rascals are reliable. Gomer is not a rascal. Therefore, Gomer is reliable. A. Valid B. Invalid

Another U-P argument No rascals are reliable. Gomer is not a rascal. Therefore, Gomer is reliable. Let p: ___ is a rascal, q: ___ is reliable prem prem conc p~q p q ~p ~q p~q ~p ~q ~p T T F F F F F q T F F T T F T F T T F T T F F F T T T T T The third row of the truth table shows that the argument is INVALID.