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Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relations on the set A = {1, 2, 3, 4}. the relation R is
- a)Reflexive
- b)transitive
- c)not symmetric
- d)a function
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relations on the...
Given, R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}.
(a) Since, (1, 1), (2, 2), (3, 3), (4, 4) ∉ R. So, R is not reflexive.
(b) Since, (1, 3) ∈ R and (3, 1) ∈ R but (1, 1) ∉ R. So, R is not transitive.
(c) Since, (2, 3) ∈ R but (3,2) ∉ R. So, B is not symmetric.
(d) Since, (2, 4) ∈ R and (2, 3) ∈ R. So, R is not a function.
(a) Since, (1, 1), (2, 2), (3, 3), (4, 4) ∉ R. So, R is not reflexive.
(b) Since, (1, 3) ∈ R and (3, 1) ∈ R but (1, 1) ∉ R. So, R is not transitive.
(c) Since, (2, 3) ∈ R but (3,2) ∉ R. So, B is not symmetric.
(d) Since, (2, 4) ∈ R and (2, 3) ∈ R. So, R is not a function.
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Community Answer
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relations on the...
Explanation:
Not Symmetric:
- A relation R is symmetric if for every (a, b) in R, (b, a) is also in R.
- In this case, (1, 3) is in R, but (3, 1) is not in R.
- Therefore, the relation R is not symmetric.
Reflexive:
- A relation R is reflexive if for every element a in A, (a, a) is in R.
- In this case, (1, 1), (2, 2), (3, 3), and (4, 4) are not in R.
- Therefore, the relation R is not reflexive.
Transitive:
- A relation R is transitive if for every (a, b) and (b, c) in R, (a, c) is also in R.
- In this case, we have (1, 3) and (3, 1) not in R, which violates transitive property.
- Therefore, the relation R is not transitive.
Summary:
- The relation R is not symmetric, reflexive, or transitive.
- Hence, the correct answer is option 'C' - not symmetric.
Not Symmetric:
- A relation R is symmetric if for every (a, b) in R, (b, a) is also in R.
- In this case, (1, 3) is in R, but (3, 1) is not in R.
- Therefore, the relation R is not symmetric.
Reflexive:
- A relation R is reflexive if for every element a in A, (a, a) is in R.
- In this case, (1, 1), (2, 2), (3, 3), and (4, 4) are not in R.
- Therefore, the relation R is not reflexive.
Transitive:
- A relation R is transitive if for every (a, b) and (b, c) in R, (a, c) is also in R.
- In this case, we have (1, 3) and (3, 1) not in R, which violates transitive property.
- Therefore, the relation R is not transitive.
Summary:
- The relation R is not symmetric, reflexive, or transitive.
- Hence, the correct answer is option 'C' - not symmetric.
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Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relations on the set A = {1, 2, 3, 4}. the relation R isa)Reflexiveb)transitivec)not symmetricd)a functionCorrect answer is option 'C'. Can you explain this answer?
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