11/9/2020 Grok | COMP30026 Practice Exam
Ques on 8 Part A (2 marks)
Ques on 8 Part A (2 marks)
We define the generalised union operator, , and the generalised intersec on operator, , as follows. For any set of sets , an object is an element of exactly when it is an element of some set in , and an object is an element of exactly when it is an element of every set in .
Let and be sets of sets. We want to express the following statements logically: a.
b.
c.
d.
using the set membership predicate possible formulas:
1. 2. 3. 4. 5. 6. 7. 8.
, together with quan fiers. Here are eight
For each of a, b, c and d, choose the correct transla on.
Note: For each of a-d, there is exactly one correct transla on among the eight formulas.
Instruc ons
ProvideyouranswerbyassigningvaluestotheHaskellvariablesa, b, c, d :: Int in the code window.
Format
https://groklearning.com/learn/unimelb-comp30026-2020-s2/prac-exam/20/ 1/1
Cheng
))z ∈ x ⇒ G ∈ z( z∀ ⇒ )y ∈ x ∧ F ∈ y( y∃( x∀ ))z ∈ x ⇒ G ∈ z( z∃ ⇒ )y ∈ x ∧ F ∈ y( y∀( x∀ ))z ∈ x ∧ G ∈ z( z∃ ⇒ )y ∈ x ∧ F ∈ y( y∃( x∀ ))z ∈ x ∧ G ∈ z( z∀ ⇒ )y ∈ x ∧ F ∈ y( y∀( x∀ ))z∈x⇒G∈z(z∃⇒)y∈x⇒ F∈y(y∃(x∀ ))z∈x⇒G∈z(z∀⇒)y∈x⇒ F∈y(y∀(x∀ ))z∈x∧G∈z(z∀⇒)y∈x⇒ F∈y(y∃(x∀ ))z∈x∧G∈z(z∃⇒)y∈x⇒ F∈y(y∀(x∀
A A⋂A
A⋃A⋂ ⋃
∈
G⋂⊆F⋂ G⋃⊆F⋂ G⋂⊆F⋃ G⋃⊆F⋃
GF