Linear Modeling and Logic Unit

4.5 Proposition and Truth Values



A proposition is a statement that is either true or false. A proposition must be in a complete sentence and must make a distinct assertion or denial.


Is each of the following a proposition? If so, is it true or false?
  1. Entering “do a barrel roll” on Google makes the page rotate.

    True

  2. “We don't need no education.”

    True

  3. No U.S. state allows its residents to vote from space.

    False

  4. "Open the pod bay doors, please, HAL."

    - DAVE BOWMAN (Keir Dullea) in 2001: A Space Odyssey (1968)

    Not a proposition.

    5. Two propositions joined together by the word "and" is called a conjunction.

    Conjunctions are only true if both propositions are true.

    Two propositions joined together by the word "or" is called a disjunction.

    Disjunctions are only false when both propositions are false.

    Determine if the following statements are true or false:
  5. Pellissippi State was founded in 1974 as State Technical Institute and it now has five campuses.

    True

  6. Pork comes from pigs and veal comes from camels.

    False

  7. Austin is the capital of Texas or Knoxville is the capital of Tennessee.

    True

  8. Verizon provides cell phone service or Comcast provides cable television service.

    True

    9. Conditionals


    An If…Then statement is called a conditional statement because it proposes something to be true (the then part of the statement) on the condition that something else is true (the if part of the statement).

    The If part of the statement is called the hypothesis and the THEN part of the statement is called the conclusion. A conditional statement is defined to be true unless a true hypothesis leads to a false conclusion.

  9. If you make an A in this class, I will buy you a new car.

    “You make an A in this class" is the hypothesis and "I buy you a new car" is the conclusion.

    In which cases did I tell the truth when I made the conditional statement?
    • You made an A in the class and I bought you a new car. (T→T)

      True

    • You made an A in the class and I did not buy you a new car. (T→F)

      False

    • You did not make an A in the class and I did not buy you a new car. (F→F)

      True

    • You did not make an A in the class and I bought you a new car. (F→T)

      True

    10. Statements Related to Conditional Statements

    Statement: If p, then q.

    Converse: If q, then p.

    Inverse: If not p, then not q.

    Contrapositive: If not q, then not p.

    Two statements are logically equivalent if they are both true OR if they are both false.

  10. Write the converse, inverse, and contrapositive of the following proposition and determine which pairs are equivalent.

    If you make an A in the class, then I will buy you a new car.

    Converse: If I buy you a new car, then you make an A in the class.

    Inverse:If you do not make an A in the class, then I will not buy you a new car.

    Contrapositive: If I will not buy you a new car, then you do not make an A in the class.