COS2661
ASSIGNMENT 2 2025
UNIQUE NO. 800278
DUE DATE: 25 JUNE 2025
, COS2661 Assignment 02
QUESTION 1 [12 marks]
1.1
Given: ∃x ¬P(x)
Tautological equivalence: ¬∀x P(x)
Explanation:
Using the logical equivalence:
∃x ¬P(x) ≡ ¬∀x P(x)
This means "There exists an x such that P(x) is false" is logically equivalent to saying "It
is not true that P(x) is true for all x."
Answer:
∃x ¬P(x) ≡ ¬∀x P(x)
1.2
Given: ∀x ¬P(x)
Tautological equivalence: ¬∃x P(x)
Explanation:
Using the logical equivalence:
∀x ¬P(x) ≡ ¬∃x P(x)
This means "P(x) is false for all x" is logically equivalent to saying "There does not exist
an x for which P(x) is true."
Answer:
∀x ¬P(x) ≡ ¬∃x P(x)
ASSIGNMENT 2 2025
UNIQUE NO. 800278
DUE DATE: 25 JUNE 2025
, COS2661 Assignment 02
QUESTION 1 [12 marks]
1.1
Given: ∃x ¬P(x)
Tautological equivalence: ¬∀x P(x)
Explanation:
Using the logical equivalence:
∃x ¬P(x) ≡ ¬∀x P(x)
This means "There exists an x such that P(x) is false" is logically equivalent to saying "It
is not true that P(x) is true for all x."
Answer:
∃x ¬P(x) ≡ ¬∀x P(x)
1.2
Given: ∀x ¬P(x)
Tautological equivalence: ¬∃x P(x)
Explanation:
Using the logical equivalence:
∀x ¬P(x) ≡ ¬∃x P(x)
This means "P(x) is false for all x" is logically equivalent to saying "There does not exist
an x for which P(x) is true."
Answer:
∀x ¬P(x) ≡ ¬∃x P(x)
