COS3761
Assignment 2
Due July 2025
,COS3761
Assignment 2: Exceptional Response
Due July 2025
Question 1: Translating English Sentences into Predicate Logic [18 Marks]
The task is to translate English sentences into predicate logic using the provided symbols
from Table 1. Each translation is accompanied by a clear explanation to ensure logical
accuracy and alignment with the sentence’s meaning.
Question 1.1: Cavaliers do not win any match except when Sam plays for them or when
they play against Aviators [3 Marks]
Translation: ¬ W( c) → ( P( s,c) ∨∃ x( M( c,x) ∧ x= a)) Symbols:
• W( x): xwins
• P( s,c): Sam plays for Cavaliers
• M( c,x): Cavaliers play against x
• a: Aviators
• c: Cavaliers
• s: Sam
Explanation: The sentence indicates that the Cavaliers ( c) do not win (¬ W( c)) unless either
Sam plays for them ( P( s,c)) or they play against the Aviators ( a) ( M( c,x) ∧ x= a). The
phrase “except when” suggests a conditional: if the Cavaliers do not win, then one of the
conditions must hold. This is expressed as an implication, where the negation of winning
implies the disjunction of the two conditions. The existential quantifier ∃ xspecifies the
match against Aviators. This structure ensures the conditional dependency is clear and
precise.
, Question 1.2: Every teenager is a football or a rugby player but no teenager plays both [3
Marks]
Translation: ∀ x( T( x) → (( F( x) ∨ R( x)) ∧¬( F( x) ∧ R( x)))) Symbols:
• T( x): xis a teenager
• F( x): xis a football player
• R( x): xis a rugby player
Explanation: The sentence has two parts: every teenager ( T( x)) is either a football player
( F( x)) or a rugby player ( R( x)), and no teenager is both. The first part is captured by
∀ x( T( x) → ( F( x) ∨ R( x))), ensuring every teenager plays at least one sport. The second
part, ∀ x( T( x) →¬( F( x)∧ R( x))), enforces mutual exclusivity by negating the conjunction of
both sports. The conjunction (∧) combines these conditions, applying the universal
quantifier to all teenagers. This translation is concise and reflects the logical constraints
clearly [?].
Question 1.3: Aviators [2 Marks]
Translation: C( a) Symbols:
• C( a): Aviators are a club
• a: Aviators
Explanation: The single word “Aviators” lacks context, suggesting an incomplete question.
The most reasonable interpretation, based on the provided symbols, is that it asserts the
Aviators ( a) are a club ( C( a)). This is a straightforward predication, assuming the sentence
intends to describe the Aviators’ status as a club. If additional context was intended, further
clarification would be required [?].
Assignment 2
Due July 2025
,COS3761
Assignment 2: Exceptional Response
Due July 2025
Question 1: Translating English Sentences into Predicate Logic [18 Marks]
The task is to translate English sentences into predicate logic using the provided symbols
from Table 1. Each translation is accompanied by a clear explanation to ensure logical
accuracy and alignment with the sentence’s meaning.
Question 1.1: Cavaliers do not win any match except when Sam plays for them or when
they play against Aviators [3 Marks]
Translation: ¬ W( c) → ( P( s,c) ∨∃ x( M( c,x) ∧ x= a)) Symbols:
• W( x): xwins
• P( s,c): Sam plays for Cavaliers
• M( c,x): Cavaliers play against x
• a: Aviators
• c: Cavaliers
• s: Sam
Explanation: The sentence indicates that the Cavaliers ( c) do not win (¬ W( c)) unless either
Sam plays for them ( P( s,c)) or they play against the Aviators ( a) ( M( c,x) ∧ x= a). The
phrase “except when” suggests a conditional: if the Cavaliers do not win, then one of the
conditions must hold. This is expressed as an implication, where the negation of winning
implies the disjunction of the two conditions. The existential quantifier ∃ xspecifies the
match against Aviators. This structure ensures the conditional dependency is clear and
precise.
, Question 1.2: Every teenager is a football or a rugby player but no teenager plays both [3
Marks]
Translation: ∀ x( T( x) → (( F( x) ∨ R( x)) ∧¬( F( x) ∧ R( x)))) Symbols:
• T( x): xis a teenager
• F( x): xis a football player
• R( x): xis a rugby player
Explanation: The sentence has two parts: every teenager ( T( x)) is either a football player
( F( x)) or a rugby player ( R( x)), and no teenager is both. The first part is captured by
∀ x( T( x) → ( F( x) ∨ R( x))), ensuring every teenager plays at least one sport. The second
part, ∀ x( T( x) →¬( F( x)∧ R( x))), enforces mutual exclusivity by negating the conjunction of
both sports. The conjunction (∧) combines these conditions, applying the universal
quantifier to all teenagers. This translation is concise and reflects the logical constraints
clearly [?].
Question 1.3: Aviators [2 Marks]
Translation: C( a) Symbols:
• C( a): Aviators are a club
• a: Aviators
Explanation: The single word “Aviators” lacks context, suggesting an incomplete question.
The most reasonable interpretation, based on the provided symbols, is that it asserts the
Aviators ( a) are a club ( C( a)). This is a straightforward predication, assuming the sentence
intends to describe the Aviators’ status as a club. If additional context was intended, further
clarification would be required [?].
