COS2661 - Assignment 2 2023

Question 1
Give the tautological equivalence of the following quantified sentences.

1.1 ¬∃x P(x)
The tautological equivalence of ¬∃x P(x) is Ɐx ¬P(x).

1.2 ∀x (P(x) ∧ Q(x))
The tautological equivalence of ∀x (P(x) ∧ Q(x)) is Ɐx P(x) ∧ Ɐx Q(x).

1.3 ∀x (P(x) → ¬Q(x))
The tautological equivalence of ∀x (P(x) ∧ Q(x)) is Ɐx P(x) ∧ Ɐx Q(x).

1.5. ¬(∃x Cube(x) ∧ ∀y Dodec(y)) ⇔
The tautological equivalence of ∀x (P(x) ∧ Q(x)) is Ɐx P(x) ∧ Ɐx Q(x).




Question 2
2.1
If Richard plays for Red Arrows, he gets injured.

FOL:
Play(richard, red) → Injured(richard)

2.2
Unless Felicity is a teacher, Vince and Richard will both play for Red Arrows.

FOL:
¬Teacher(felicity) → (Play(vince, red) ∧ Play(richard, red))

2.3
Everyone gets injured when Vince plays for Blue Bucks.

FOL: ∀x (Play(x, blue) → Injured(x))

2.4
No teachers are soccer players.

FOL: ¬∃x (Teacher(x) ∧ Player(x))

2.5
If we assume that Vince plays for Blue Bucks, Felicity also plays for Blue Bucks but Richard plays
for Red Arrows.

FOL:
Play(vince, blue) → (Play(felicity, blue) ∧ ¬Play(richard, blue))