Hurley 5.2


  1. Write the following compound statements in symbolic form, then use your knowledge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
  2. Nixon resigned the presidency and Lincoln wrote the Gettysburg Address.
  3. Hitler ran the Third Reich and Nixon did not resign the presidency.
  4. Alexander the Great civilized America if Napoleon ruled France.
  5. Lincoln wrote the Gettysburg Address if and only if France bombed Pearl Harbor.
  6. If Hitler ran the Third Reich, then either Custer was killed by the Indians or Einstein discovered aspirin.
  7. Lincoln’s having written the Gettysburg Address is a sufficient condition for Alexander the Great’s having civilized America if and only if Washington’s being assassinated is a necessary condition for Custer’s having been killed by the Indians.
  8. It is not the case that Custer was killed by the Indians unless both Nixon resigned the presidency and Edison invented the telephone.

III. Determine the truth values of the following symbolized statements. Let A, B, and C be true and X, Y, and Z be false. Circle your answer.

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  1. B • ~ Y
  2. ~ C v Z
  3. Y ↄ ~A
  4. B ≡ Y
  5. ~ (A • ~ Z)
  6. A ↄ ~ (Z v ~ Y)
  7. ~ (X v ~ B) • (~ Y v A)
  8. (C ≡ ~A) v (Y ≡ Z)
  9. ~ [(B v ~C) • ~ (X v ~Z)]
  10. (X ↄ Z) ↄ [(B ≡ ~X) • ~ (C v ~A)]
  11. ~ [(A ≡ X) v (Z ≡ Y)] v [(~ Y ↄ B) • (Z ↄ C)]
  12. ~ { ~ [(C v ~B) • (Z v ~A)] • ~[ ~(B v Y) • (~X v Z)]}


  1. When possible, determine the truth values of the following symbolized statements. Let A and B be true, Y and Z false. P and Q have unknown truth value. If the truth value of the statement cannot be determined, write “undetermined.”
  2. Q v Z
  3. Q • A
  4. Z ↄ Q
  5. P ≡ ~P
  6. (P ↄ A) ≡ (Q ↄ B)
  7. ~ (P ↄ Y) v (Z ↄ Q)
  8. [(Z ↄ P) ↄ P] ↄ P






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