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Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?
  • a)
    R is reflexive and symmetric, but not transitive
  • b)
    R is symmetric and transitive, but not reflexive
  • c)
    R is reflexive and transitive, but not symmetric
  • d)
    R is neither reflexive nor transitive, but symmetric
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2,...
Given X = {1, 2, 3, 4} and R = [(1, 1), (2, 2), (3, 3), (1, 2), (2,1), (2, 3), (3, 2)}
Reflexive Property states that for every real number x, x=x.
Here (1,1) ∈ R, (2,2) ∈ R, (3,3) ∈ R, but (4,4) ∉ R. So, R is not Reflexive.
Symmetric Property states that for all real numbers x and y, if x=y, then y=x.
(1, 2) ∈ R, (2, 1) ∈ R and, (2, 3) ∈ R, (3,2) ∈ R
So, R is symmetric.
Transitive Property states that for all real
numbers x, y and z, if x=y and y=z, then x=z.
Here (1, 2) ∈ R, (2, 1) ∈ R and (1, 1) ∈ R,
Similarly, (2, 3) ∈ R, (3, 2) ∈ R, (2, 2) ∈ R
But for (1, 2) ∈ R, (2, 3) ∈ R, (1, 3) ∉ R
So, R is not transitive.
Thus, R is neither reflexive nor transitive, but symmetric.
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Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is symmetric and transitive, but not reflexivec)R is reflexive and transitive, but not symmetricd)R is neither reflexive nor transitive, but symmetricCorrect answer is option 'D'. Can you explain this answer?
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Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is symmetric and transitive, but not reflexivec)R is reflexive and transitive, but not symmetricd)R is neither reflexive nor transitive, but symmetricCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is symmetric and transitive, but not reflexivec)R is reflexive and transitive, but not symmetricd)R is neither reflexive nor transitive, but symmetricCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose X = {1, 2, 3, 4} and R is a relation on X. If R = [(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}, then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is symmetric and transitive, but not reflexivec)R is reflexive and transitive, but not symmetricd)R is neither reflexive nor transitive, but symmetricCorrect answer is option 'D'. Can you explain this answer?.
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