ASSIGNMENT
Determine which of the following are not well-formed formulas.
1. (S ∼T)¡(∼U W) ●
2.∼(K¡L) (⊃G¡H)
3. (E∼F)¡(WKX)
4. (B⊃∼T)K∼(∼C⊃U)
5. (FK∼Q) (A⊃E¡T)
7. [(D ¡ Q)⊃(P¡ E)]¡ [A⊃( H)] ●●
8. M(N⊃Q)¡(∼C D)●●
9. ∼(F¡∼G)⊃[(AKE) ∼H]
10. (RKS● T)⊃∼(∼W● ∼X)IV.
Construct compound propositions involving at least three simple propositions about the following topics. Then, symbolize your propositions as per Parts I and II of this exercise.
1. Political figures
2. NFL teams
3. Corporations
4. Brands of automobiles
5. Music or film celebrities
Write the following compound statements in symbolic form, then use your knowl- edge of the historical events referred to by the simple statements to determine the truth value of the compound statements.
1. It is not the case that Hitler ran the Third Reich.
2. Nixon resigned the presidency and Lincoln wrote the Gettysburg Address.
3. France bombed Pearl Harbor, or Lindbergh crossed the Atlantic.
4. Hitler ran the Third Reich and Nixon did not resign the presidency.
5. Edison invented the telephone, or Custer was killed by the Indians.
6. Julius Caesar conquered America if Napoleon ruled France.
7. Washington was assassinated only if Edison invented the telephone.
8. Lincoln wrote the Gettysburg Address if and only if France bombed Pearl
Harbor.
9. It is not the case that either Julius Caesar conquered America or Washington was assassinated.
10. If Hitler ran the Third Reich, then either Custer was killed by the Indians or Einstein discovered aspirin.
11. Either Lindbergh crossed the Atlantic and Edison invented the telephone or both Nixon resigned the presidency and it is false that Edison invented the telephone.
12. Lincoln’s having written the Gettysburg Address is a sufficient condition for Julius Caesar’s having conquered America if and only if Washington’s being assassinated is a necessary condition for Custer’s having been killed by the Indians.
13. Both Hitler ran the Third Reich and Lindbergh crossed the Atlantic if neither Einstein discovered aspirin nor France bombed Pearl Harbor.
14. It is not the case that Custer was killed by the Indians unless both Nixon resigned the presidency and Edison invented the telephone.
15. Custer was killed by the Indians, and Lincoln wrote the Gettysburg Address only if either Washington was assassinated or Julius Caesar conquered America
