COS3751 Assignment 3 (717989)|COMPLETE ANSWERS|- DUE 15 August 2025

COS3751
Assignment 3

Unique No: 717989
DUE 15 August 2025

, COS3751 ASSIGNMENT 03
Student Number: [Your Student Number]
Name: [Your Name]
Due Date: 15 August 2025




Question 1 [10]

(a) Emily is either a surgeon or a lawyer (but not both).

(Surgeon(Emily) ∨ Lawyer(Emily)) ∧ ¬(Surgeon(Emily) ∧ Lawyer(Emily)).

(Emily is a surgeon or a lawyer, and not both.)

(b) All surgeons are doctors.

∀𝑥 (Surgeon(𝑥) → Doctor(𝑥)).

(For every person 𝑥, if 𝑥 is a surgeon then 𝑥 is a doctor.)

(c) Joe does not have a lawyer (i.e. he is not the customer of any lawyer).

¬∃𝑦 (Lawyer(𝑦) ∧ Customer(Joe, 𝑦)).

(There is no person 𝑦 who is a lawyer and of whom Joe is a customer.)

(d) There exists a lawyer all of whose customers are doctors.

∃𝑦 (Lawyer(𝑦) ∧ ∀𝑥 (Customer(𝑥, 𝑦) → Doctor(𝑥)) ).

(There is a lawyer 𝑦 such that every customer 𝑥 of 𝑦 is a doctor.)

(e) Every surgeon has a lawyer.

∀𝑥 (Surgeon(𝑥) → ∃𝑦 ( Lawyer(𝑦) ∧ Customer(𝑥, 𝑦))).

(For every surgeon 𝑥 there exists some 𝑦 who is a lawyer and whom 𝑥 is a customer
of.)