Uploaded a document with statements I updated to formal logic. Just looking to have my answers reviewed. Had some trouble with the notation of number 4 and 5.

Page of 8 ZOOM "Stable Marriage" Problem A well-known problem in the field of Computer Science known as the "Stable Marriage problem. As it was defined, the problem describes a scenario where a set of men and an equally sized set of women are to be matched up for marriage while taking into account their preference of partners. In a more general case, this problem can be defined as the following: Suppose you have two distinct sets of elements, denoted A and B. Both sets have exactlyn elements. Each element in set A is to be paired with another element in set B. Prior to pairing, all elements in A give high-to-low preference ranking showing which elements in B they want to be paired with, and vice-versa. A "stable pairing" is a set (denoted S) in which the following conditions hold true: 1. The set S must be a subset of Ax B (cartesian product of A and B) 2. All elements in set A have a corresponding element in set B such that the pair (a, b) is an element of S 3. All elements in set B have a corresponding element in set A such that the pair (a, b) is an element of S 4. There are no two pairs (a, b) and (a', b') in such that b'is higher preference for a than b, and a is higher preference for b'than a' (in this case, since a and b'both prefer each their assigned match, they will choose to break their match in favor of a match (a, b)) 5. There are no two pairs (a, b) (a', b') in S such that a'is higher preference for b than a, and b is higher preference for a' than b' (again, in this case band a' would break their assigned match in favor of a match (a', b) other to For example, consider students in CS 3345 and CS 3353 as two distinct sets of people (assume that you can't enroll in both at the same time). Your sets may look like: A = { "Alex", "Bob" "Charles"} B = { "Devin", "Erik", "Frank" } Where A = CS 3345 and B = CS 3353. A joint project between the two classes requires forming pairs of students containing one student from each class. Prior to creating pairs, each student was tasked with defining who they want to work with, in order of high to low preference: Alex: Devin, Frank, Erik Bob: Frank, Erik, Devin Devin: Charles, Bob, Alex Erik: Bob, Charles, Alex an Stable Marciag. Problem 1) The vet I must be a oubret ) of AxB (cartoon product of A and B) Se (A&B) 2) All elements in set A have corresponding element in red By such that the (Up EA7 EB):(p,965 3) All elemento Jet B have corresponding element in Set o such that the (a, b) is an element of s (Upe B-734 A): (p.net element of pair (a, b) is b) 3 in A pair are no s a CA a since 4) Thre two pars (a,b) and (a, b) in s such that b' is higher preference for than b, and jo higher preference for b' than a f in this case, a and b' both prefer. eachother to their assigned match, they will choose to break their match favor of match Ca. 6)). (2.b)^(a'b') 5 bis higher pretorne for b,1 high-preference for b than a' at a than are no such 15 higher s) There two pairs Ca, b) and Cai, b') in 5, S that al preference for b than a and b is higher preference for a' than b. Jane questic precious a ch as Page of 8 ZOOM "Stable Marriage" Problem A well-known problem in the field of Computer Science known as the "Stable Marriage problem. As it was defined, the problem describes a scenario where a set of men and an equally sized set of women are to be matched up for marriage while taking into account their preference of partners. In a more general case, this problem can be defined as the following: Suppose you have two distinct sets of elements, denoted A and B. Both sets have exactlyn elements. Each element in set A is to be paired with another element in set B. Prior to pairing, all elements in A give high-to-low preference ranking showing which elements in B they want to be paired with, and vice-versa. A "stable pairing" is a set (denoted S) in which the following conditions hold true: 1. The set S must be a subset of Ax B (cartesian product of A and B) 2. All elements in set A have a corresponding element in set B such that the pair (a, b) is an element of S 3. All elements in set B have a corresponding element in set A such that the pair (a, b) is an element of S 4. There are no two pairs (a, b) and (a', b') in such that b'is higher preference for a than b, and a is higher preference for b'than a' (in this case, since a and b'both prefer each their assigned match, they will choose to break their match in favor of a match (a, b)) 5. There are no two pairs (a, b) (a', b') in S such that a'is higher preference for b than a, and b is higher preference for a' than b' (again, in this case band a' would break their assigned match in favor of a match (a', b) other to For example, consider students in CS 3345 and CS 3353 as two distinct sets of people (assume that you can't enroll in both at the same time). Your sets may look like: A = { "Alex", "Bob" "Charles"} B = { "Devin", "Erik", "Frank" } Where A = CS 3345 and B = CS 3353. A joint project between the two classes requires forming pairs of students containing one student from each class. Prior to creating pairs, each student was tasked with defining who they want to work with, in order of high to low preference: Alex: Devin, Frank, Erik Bob: Frank, Erik, Devin Devin: Charles, Bob, Alex Erik: Bob, Charles, Alex an Stable Marciag. Problem 1) The vet I must be a oubret ) of AxB (cartoon product of A and B) Se (A&B) 2) All elements in set A have corresponding element in red By such that the (Up EA7 EB):(p,965 3) All elemento Jet B have corresponding element in Set o such that the (a, b) is an element of s (Upe B-734 A): (p.net element of pair (a, b) is b) 3 in A pair are no s a CA a since 4) Thre two pars (a,b) and (a, b) in s such that b' is higher preference for than b, and jo higher preference for b' than a f in this case, a and b' both prefer. eachother to their assigned match, they will choose to break their match favor of match Ca. 6)). (2.b)^(a'b') 5 bis higher pretorne for b,1 high-preference for b than a' at a than are no such 15 higher s) There two pairs Ca, b) and Cai, b') in 5, S that al preference for b than a and b is higher preference for a' than b. Jane questic precious a ch as