Question 1:

A = there have been three previous female Presidents of the United States F

B = peanuts contain saturated fat T

C = Beyonc ́e performed at the Superbowl 50 halftime show T

D = Luke Skywalker will be unveiled as the father of Rey in Episode VIII U

  1. A ∨ B = T
  2. A ∧ B = F
  3. A ⇒ B = T
  4. A ⊕ B = T
  5. B ∨ A = T
  6. B ∧ A = F
  7. B ⇒ A = F
  8. B ⊕ A = T
  9. C ∨ D = T
  10. (¬C) ∧ (¬D) = F ∧ U = F
  11. A ⇒ D = F ⇒ U = F
  12. A ⇒ A = T
  13. D ⇒ D = (T ⇒ T) or (F ⇒ F) = T
  14. ¬((¬A) ∧ (¬B)) = ¬(T ∧ F) = ¬(F) = T
  15. ¬((¬B) ∧ (¬C)) = ¬(F ∧ F) = ¬(F) = T
  16. ¬((¬A) ∧ (¬B) ∧ (¬C)) = ¬(T ∧ F ∧ F) = ¬(F) = T
  17. D ∧ ¬D = (T ∧ F) or (F ∧ T) = F
  18. D ∨ ¬D = (T ∨ F) or (F ∨ T) = T

Question 2:

((¬G) ⊕ H) ⇔ ((G ∨ ¬I) ∧ F )

F G H I ¬G (¬G) ⊕ H ¬I G ∨ ¬I (G ∨ ¬I) ∧ F ((¬G) ⊕ H) ⇔ ((G ∨ ¬I) ∧ F )
T T T T F T F T T T
T T T F F T T T T T
T T F T F F F T T F
T T F F F F T T T F
T F T T T F F F F T
T F T F T F T T T F
T F F T T T F F F F
T F F F T F T T T F
F T T T F T F T F F
F T T F F T T T F F
F T F T F F F T F T
F T F F F F T T F T
F F T T T F F F F T
F F T F T F T T F T
F F F T T T F F F F
F F F F T F T T F T

Question 3:

Celebrity(x) — the proposition that x is well-known in pop American culture

Wedded(x,y) — the proposition that x and y at one point in their lives got married

Married(x,y) — the proposition that x and y are currently married

Single(x) — the proposition that x is not currently married

Divorced(x,y) — the proposition that x and y at one point in their lives got divorced

  1. Donald Knuth is not a celebrity.

¬Celebrity(Donald Knuth)

  1. Kim Kardashian is a celebrity.

Celebrity(Kim Kardashian)

  1. Kim Kardashian is married to a celebrity.

∃ x Celebrity(x) ∧ Married(Kim Kardashian, x)

  1. Kim Kardashian wedded two different celebrities.

∃ x ∃ y Celebrity(x) ∧ Celebrity(y) ∧ Wedded(Kim Kardashian, x) ∧ Wedded(Kim Kardashian, y)

  1. Some celebrities marry other celebrities, while some just marry ordinary folk.

∃ x ∃ y ∃ z ∃ u Celebrity(x) ∧ Celebrity(y) ∧ Celebrity(z) ∧ ¬Celebrity(u) ∧ Wedded(x,y) ∧ Wedded(z,u)

  1. If you’re married, then you’re not single.

∀ x ∀ y Married(x,y) ⇒ ¬Single(x)

  1. It’s possible to have once been married, and never divorced, and yet be currently single.

¬(∀ x ∀ y Wedded(x,y) ∧ ¬Divorced(x,y) ⇒ ¬Single(x))