1.Find the total number of binary operations on a set containing 5 elements. 2.Given a relation R on Z defined by mRn 3|(m-n) for all m,neZ. Find the equivalent class determined by 4. 3.Give an example of a semigroup which is not a monoid.

Q: Define an equivalence relation R on the set A = {2,3,4,...,20} by mRn if the largest prime divisor…

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Q: 3.(1) List all the partitions of the set S = {1, 2, 3, 4}. (2) From (1), determine how many…

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Q: 1. Prove that the relation "divides" on the integers is reflexive and transitive.

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: a. xRy x C y

A: Since you have asked multiple question, we can solve first question for you. If you want other…

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Q: 9. List the ordered pairs in the equivalence relation on A = {1, 2, 3, 4, 5} associated with these…

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Q: 5. Consider the relation in N given by n~m if n and m have the same number of digits in the decimal…

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Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: (a) Show that R is an equivalence relation. (b) List three members of each of the equivalence…

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Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

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Q: Let R be a binary relation on A={1,2,3,43 defined a is related with b) if a²-b² is divisble by 3.…

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Q: 6. Find all elements of the equivalence class of 12 under congruence modulo 5.

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