How to solve this problem 1. Write down all of the properties that each of the following binary relations satisfiesthe four properties reflexive, symmetric, antisymmetric, and transitive.fromamongExplain your answer.a. The "has a common national language with" relation on countries: (a, b) is inthe relation if a and b have a common national languageb. The relation on people that relates people with bachelor's degrees in computerscience: (a, b) is in the relation iff both a and b have a bachelor's degree incomputer science, or neither a nor b have a bachelor's degree in computerscience.

Name: How to solve this problem 1. Write down all of the properties that eac
Uploaded: 2024-03-05T11:52:21.000Z
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Description: How to solve this problem 1. Write down all of the properties that each of the following binary relations satisfiesthe four properties reflexive, symmetric, antisymmetric, and transitive.fromamongExplain your answer.a. The "has a common national lang

The objective is: (a) To write down all the properties for “has a common language with” relation on the countries from among the five properties Reflexive, symmetric, transitive, irreflexive and antisymmetric. (b) To write down all of the properties for the relation on people that relate people with bachelor’s degrees in computer science from among the five properties reflexive, symmetric, transitive, irreflexive, and antisymmetric.(a) Consider a binary relation R on a set A. R is reflexive, if xRx for all x∈A. A country X will have always same common language. Hence, R is Reflexive. For a binary relation R on a set A, R is symmetric if xRy⇒yRx for all x, y∈A If language of country X and Y are same, then it can be said that language of country Y and X are same. Hence, R is symmetric. For a binary relation R on a set A, R is transitive if xRy and yRz⇒xRz for all x, y, z∈A. If country X and Y have same common language and country Y and Z have same common language. Then it does not mean that country X and Y also have same common language. Hence, R is not transitive. For a binary relation R on a set A, R is irreflexive if x, x∉R for all x∈A. There cannot be any case in which a country has different common language. Hence, R is not irreflexive. For a binary relation R on a set A, R is anti-symmetric if xRy and xRy⇒x=y for all x, y∈A. If two countries have same common language, then it does not mean that both the countries are same. Hence, R is not anti-symmetric. Hence, R is reflexive and symmetric.(b) For a binary relation R on a set A, R is reflexive if xRx for all x∈A. A person with bachelor’s degree in computer science always relates to itself. Hence, R is reflexive. For a binary relation R on a set A, R is symmetric if xRy⇒yRx for all x, y∈A. If person X and person Y both have Bachelor’s degree in computer science, then X is related to Y, and Y is also related to X because they both have bachelor’s degree. Hence, R is symmetric. For a binary relation R on a set A, R is transitive if xRy and yRz⇒xRz for all x, y, z∈A. If X have bachelor’s degree in computer science and Y also have bachelor’s degree in computer science, then XRB. Also, if Y and Z are also related in same manner, then X and Z are also related to each other. Because they both have bachelor’s degree in computer science. Hence, R is transitive. For a binary relation R on a set A, R is irreflexive if x, x∉Rfor all x∈A. There cannot be any condition, in which same person holding a bachelor’s degree in computer science is not related to itself. Hence, R is not irreflexive. A binary relation R on A is antisymmetric if xRy and yRx⇒x=y for all x, y∈A. If two people hold the bachelor’s degree in computer science, then it does not mean that two persons are same. Hence, R is not antisymmetric. Hence, R is reflexive, transitive and symmetric