Part IV: Exercises

Give the variable notation of the disjunctive proposition. Explain, in your own words, what variable notation is, and how it applies to the disjunctive proposition.

Give three examples of true disjunctive propositions. State whether each uses the exclusive or inclusive “or.” Say what it means to take that interpretation of “or.” 

Ex. “Pigs can fly or oaks are trees.” This example uses an exclusive “or.” In other words, it is either the case that (1) pigs can fly or (2) oaks are trees, but not both (1) and (2). (Note that the student can interpret this with an inclusive “or” as well.)

 Determine whether the following compound propositions are true or false, and justify your answer. Also, specify if you are interpreting the sentence to be an inclusive or exclusive disjunction where needed.

Ex. Birds have wings or Pigs have wings. 

Answer: True, as only the first of the two disjuncts is true, however the rules of disjunction state that only one of the two disjuncts must be true to render the whole proposition true. 

1. Puppies are cute or kittens are cute.
2. The Atlantic Ocean is green or Canada is in South America.
3. Balloons can float or humans are primates.
4. Sharks cannot smell blood or humans have five left feet.
5. Aristotle was the first formal logician or Aristotle was not the first formal logician.