## 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

- A ∨ B = T
- A ∧ B = F
- A ⇒ B = T
- A ⊕ B = T
- B ∨ A = T
- B ∧ A = F
- B ⇒ A = F
- B ⊕ A = T
- C ∨ D = T
- (¬C) ∧ (¬D) = F ∧ U = F
- A ⇒ D = F ⇒ U = F
- A ⇒ A = T
- D ⇒ D = (T ⇒ T) or (F ⇒ F) = T
- ¬((¬A) ∧ (¬B)) = ¬(T ∧ F) = ¬(F) = T
- ¬((¬B) ∧ (¬C)) = ¬(F ∧ F) = ¬(F) = T
- ¬((¬A) ∧ (¬B) ∧ (¬C)) = ¬(T ∧ F ∧ F) = ¬(F) = T
- D ∧ ¬D = (T ∧ F) or (F ∧ T) = F
- 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

- Donald Knuth is not a celebrity.

¬Celebrity(Donald Knuth)

- Kim Kardashian is a celebrity.

Celebrity(Kim Kardashian)

- Kim Kardashian is married to a celebrity.

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

- Kim Kardashian wedded two different celebrities.

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

- 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)

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

∀ x ∀ y Married(x,y) ⇒ ¬Single(x)

- 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))