Problem 2. This problem is about composing relations and inverse of a relation. Definition 1. Suppose...

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Problem 2. This problem is about composing relations and inverse of a relation. Definition 1. Suppose R: A B and S: B →→ C (note the domains and co-domains on which these relations are defined). Then we can construct a new relation SoR, called the composition relation from A-C as follows: (a, c) ESOR Em EB such that (a,m) ≤R and (m, c) ES. Let R: R →→ R be the relation defined by R = {(x,y)]y = 7x-10} and 9: R →→ R be a relation defined by S = {(x,y)|y=−5x+2}. 1. Find RoS, S OR and ROR. Your answers must be in the form RoS = {(x,y) | appropriate conditions}. 2. Suppose X:A-B, we define the inverse relation X-¹:BA as follows: K−¹ = {(b,a)|(a,b) ≤K}. In other words, we say b is related to a via K-¹ if a is related to b via K. Using this definition and the relations R and S given at the beginning of this problem, find the following relations: Problem 2. This problem is about composing relations and inverse of a relation. Definition 1. Suppose R: A B and S: B →→ C (note the domains and co-domains on which these relations are defined). Then we can construct a new relation SoR, called the composition relation from A-C as follows: (a, c) ESOR Em EB such that (a,m) ≤R and (m, c) ES. Let R: R →→ R be the relation defined by R = {(x,y)]y = 7x-10} and 9: R →→ R be a relation defined by S = {(x,y)|y=−5x+2}. 1. Find RoS, S OR and ROR. Your answers must be in the form RoS = {(x,y) | appropriate conditions}. 2. Suppose X:A-B, we define the inverse relation X-¹:BA as follows: K−¹ = {(b,a)|(a,b) ≤K}. In other words, we say b is related to a via K-¹ if a is related to b via K. Using this definition and the relations R and S given at the beginning of this problem, find the following relations:

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