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COS2661 - Assignment 3 2023
- Course
- COS2661 - Formal Logic II
- Institution
- University Of South Africa (Unisa)
Complete Solutions to COS2661 Assignment 3 for the year 2023.
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By: hiltontutorials • 1 year ago
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Question 1Give the tautological equivalence of the following quantified sentences.
1.1
∀x (dog(x) ∧ Brown(x) → hairy(x))
Explanation:
• ∀x: For every object x.
• dog(x): x is a dog.
• Brown(x): x is brown.
• hairy(x): x is hairy.
• →: Implication, meaning "implies" or "if...then."
• ∧: Conjunction, meaning "and."
1.2
∃x (Corgi(x) ∧ ∀y (Person(y) → Loves(x, y)))
Explanation:
• ∃x: There exists an object x.
• (Corgi(x) ∧ ∀y (Person(y) → Loves(x, y))): The object x is a Corgi and it loves every
individual y who is a person.
1.3
∀x ∃y (Corgi(y) ∧ Loves(x, y))
Explanation:
• ∀x: For all x (for every person).
• ∃y: There exists a y (at least one Corgi).
• Corgi(y): y is a Corgi.
• Loves(x, y): x loves y.
1.4
∀x ∀y (Pancakes(x) ∧ Pancakes(y) ∧ x ≠ y) → TasteSimilar(x, y)
Explanation:
• "For all x and y, if x and y are both pancakes and they are not the same (x ≠ y), then x
and y taste similar."
• In simpler terms, the statement asserts that every pair of distinct pancakes taste similar to
each other.
1.5
∀x ∃y₁ ∃y₂ (Person(x) → (y₁ ≠ y₂ ∧ Knows(x, y₁) ∧ Knows(x, y₂)))
Explanation:
• ∀x - For all x (for every person x)
• ∃y₁ - There exists a person y₁
• ∃y₂ - There exists another person y₂
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