3. [15] The abstract data type (ADT) Set(Elm) represent sets. Accordingly, the following is a possible set of operators: new: Set set: Elm Set in: Set x Elm→ Bool empty: Set →Bool count: SetInteger delete: Set x Elm Set create a new, empty set create a singleton set true iff a value is in a set true iff the set is empty returns the number of values in the set removes a value from a set intersect: Set x Set Set returns the intersection of two sets union: Set x Set Set returns the union of two sets with no duplicate values (a) [5] Identify between the operators enumerated above a minimal set of constructors and justify your choice. (b) [10] Provide axioms for the operators empty, count, and delete.

C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter13: Overloading And Templates
Section: Chapter Questions
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3. [15] The abstract data type (ADT) Set(Elm) represent sets. Accordingly, the following is a
possible set of operators:
new: Set
set: Elm Set
in: Set x Elm→ Bool
empty: Set →Bool
count: SetInteger
delete: Set x Elm Set
create a new, empty set
create a singleton set
true iff a value is in a set
true iff the set is empty
returns the number of values in the set
removes a value from a set
intersect: Set x Set
Set
returns the intersection of two sets
union: Set x Set
Set
returns the union of two sets with no duplicate values
(a) [5] Identify between the operators enumerated above a minimal set of constructors and
justify your choice.
(b) [10] Provide axioms for the operators empty, count, and delete.
Transcribed Image Text:3. [15] The abstract data type (ADT) Set(Elm) represent sets. Accordingly, the following is a possible set of operators: new: Set set: Elm Set in: Set x Elm→ Bool empty: Set →Bool count: SetInteger delete: Set x Elm Set create a new, empty set create a singleton set true iff a value is in a set true iff the set is empty returns the number of values in the set removes a value from a set intersect: Set x Set Set returns the intersection of two sets union: Set x Set Set returns the union of two sets with no duplicate values (a) [5] Identify between the operators enumerated above a minimal set of constructors and justify your choice. (b) [10] Provide axioms for the operators empty, count, and delete.
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