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A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?
  • a)
    R is not an equivalence relation
  • b)
    R is an equivalence relation having 1 equivalence class
  • c)
    R is an equivalence relation having 2 equivalence classes
  • d)
    R is an equivalence relation having 3 equivalence classes
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A relation R is defined on the set of integers as xRy if f(x + y) is e...
There are 2 2 equivalence classes. 1) All odd integers. (Reflexive as sum of two even is even, Symmetric and Transitive as + operation is Symmetric and Transitive) 2) All Even Integers. (Reflexive as sum of two odd is even, Symmetric and Transitive as + operation is Symmetric and Transitive)
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A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?a)R is not an equivalence relationb)R is an equivalence relation having 1 equivalence classc)R is an equivalence relation having 2 equivalence classesd)R is an equivalence relation having 3 equivalence classesCorrect answer is option 'C'. Can you explain this answer?
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A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?a)R is not an equivalence relationb)R is an equivalence relation having 1 equivalence classc)R is an equivalence relation having 2 equivalence classesd)R is an equivalence relation having 3 equivalence classesCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?a)R is not an equivalence relationb)R is an equivalence relation having 1 equivalence classc)R is an equivalence relation having 2 equivalence classesd)R is an equivalence relation having 3 equivalence classesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?a)R is not an equivalence relationb)R is an equivalence relation having 1 equivalence classc)R is an equivalence relation having 2 equivalence classesd)R is an equivalence relation having 3 equivalence classesCorrect answer is option 'C'. Can you explain this answer?.
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