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Truth Tables

Completion requirements

Read these sections to learn how to interpret, make, and apply truth tables to sentential logic formulas, note conditional statements in sentential logic, and translate the word "unless" into sentential logic. Be sure to note the difference between an antecedent and a consequent and between a necessary and sufficient condition.

Complete the exercises, checking your answers against the key.

Exercise

Answers

  1. T ⊃ I (T = The Tigers will win; I = The Indians will lose their star pitcher)
  2. H ⊃ P (P = Tom will pass the class; H = Tom does all of his homework)
  3. R ⊃ G (R = The car will run; G = The car has gas)
  4. A ⊃ C (A = You are asking me about your grade; C = You care about your grade)
  5. F ⋅ (T ⊃ B) (F = Frog will swim without his bathing suit; T = Toad will swim; B = Toad is wearing a bathing suit)
  6. ~O ⊃ M (O = Obama is not a U.S. citizen; M = I am a monkey's uncle)
  7. T ⊃ ~F (T = Toad wears his bathing suit; F = Toad wants Frog to see him in his bathing suit)
  8. ~P ⊃ (S v L) (P = Tom passes his exam; S = Tom is stupid; L = Tom is lazy)
  9. H ⊃ W (W = Bekele will win the race; H = Bekele stays healthy)
  10. (S v I) ⊃ ~W (S = Bekele is sick; I = Bekele is injured; W = Bekele will win the race)
  11. P ⊃ (C ⋅ ~S) (P = Bob will become president; C = Bob runs a good campaign; S = Bob says something stupid)
  12. T ⊃ P (T = That plant has three leaves; P = That plant is poisonous)
  13. P ⊃ T (T = That plant has three leaves; P = That plant is poisonous)
  14. P ⊃ T (T = That plant has three leaves; P = That plant is poisonous)
  15. P ⊃ T (T = That plant has three leaves; P = That plant is poisonous)
  16. N ⊃ O (O = Olga will swim in the open water; N = There is a shark net present)
  17. O ⊃ N (O = Olga will swim in the open water; N = There is a shark net present)
  18. O ⊃ B (O = Olga is swimming; B = Olga is wearing a bathing suit)
  19. N ⊃ ~B (N = Olga is in Nice; B = Olga wears a bathing suit)
  20. T ⊃ B (T = Terrence pulls Philip's finger; B = Something bad will happen)
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