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An integer m is said to be related to another integer n, if m is a multiple of n. Then, the relation is
- a)reflexive and symmetric
- b)reflexive and transitive
- c)symmetric and transitive
- d)equivalence relation
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An integer m is said to be related to another integer n, if m is a mul...
For any integer n, we have n | n => nRn
So, nRn for all n ∈ Z implies R is reflexive
Now, 2|6 but 6 + 2,
implies (2 ,6) ∈ R but (6,2) ∉ R
So, R is not symmetric.
Let (m, n) ∈ R and (n , p) ∈ R
Then,
implies m | p => (m,p) ∈ R
So, R is transitive.
Hence, R is reflexive and transitive but it is not symmetric.
So, nRn for all n ∈ Z implies R is reflexive
Now, 2|6 but 6 + 2,
implies (2 ,6) ∈ R but (6,2) ∉ R
So, R is not symmetric.
Let (m, n) ∈ R and (n , p) ∈ R
Then,
implies m | p => (m,p) ∈ R
So, R is transitive.
Hence, R is reflexive and transitive but it is not symmetric.
Most Upvoted Answer
An integer m is said to be related to another integer n, if m is a mul...
For any integer n, we have n | n => nRn
So, nRn for all n ∈ Z implies R is reflexive
Now, 2|6 but 6 + 2,
implies (2 ,6) ∈ R but (6,2) ∉ R
So, R is not symmetric.
Let (m, n) ∈ R and (n , p) ∈ R
Then,
implies m | p => (m,p) ∈ R
So, R is transitive.
Hence, R is reflexive and transitive but it is not symmetric.
So, nRn for all n ∈ Z implies R is reflexive
Now, 2|6 but 6 + 2,
implies (2 ,6) ∈ R but (6,2) ∉ R
So, R is not symmetric.
Let (m, n) ∈ R and (n , p) ∈ R
Then,
implies m | p => (m,p) ∈ R
So, R is transitive.
Hence, R is reflexive and transitive but it is not symmetric.
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Community Answer
An integer m is said to be related to another integer n, if m is a mul...
Reflexive Property:
The reflexive property states that every element is related to itself. In the context of the given relation, it means that every integer m is related to itself because m is a multiple of m.
Symmetric Property:
The symmetric property states that if m is related to n, then n is also related to m. In the given relation, if m is a multiple of n, it implies that n divides m completely. Hence, the relation is symmetric.
Transitive Property:
The transitive property states that if m is related to n and n is related to p, then m is related to p. In the given relation, if m is a multiple of n and n is a multiple of p, it implies that m is also a multiple of p. Therefore, the relation is transitive.
Explanation of the Correct Answer:
The correct answer is option B because the relation is reflexive and transitive. It is not symmetric because the relation does not hold if m and n are not multiples of each other. For example, if m = 6 and n = 5, then m is not a multiple of n, and hence the relation does not hold.
In order to be an equivalence relation, a relation must be reflexive, symmetric, and transitive. As the given relation is not symmetric, it cannot be an equivalence relation. Therefore, option D is not the correct answer.
Summary:
The relation described in the question is reflexive and transitive, but not symmetric. Therefore, the correct answer is option B.
The reflexive property states that every element is related to itself. In the context of the given relation, it means that every integer m is related to itself because m is a multiple of m.
Symmetric Property:
The symmetric property states that if m is related to n, then n is also related to m. In the given relation, if m is a multiple of n, it implies that n divides m completely. Hence, the relation is symmetric.
Transitive Property:
The transitive property states that if m is related to n and n is related to p, then m is related to p. In the given relation, if m is a multiple of n and n is a multiple of p, it implies that m is also a multiple of p. Therefore, the relation is transitive.
Explanation of the Correct Answer:
The correct answer is option B because the relation is reflexive and transitive. It is not symmetric because the relation does not hold if m and n are not multiples of each other. For example, if m = 6 and n = 5, then m is not a multiple of n, and hence the relation does not hold.
In order to be an equivalence relation, a relation must be reflexive, symmetric, and transitive. As the given relation is not symmetric, it cannot be an equivalence relation. Therefore, option D is not the correct answer.
Summary:
The relation described in the question is reflexive and transitive, but not symmetric. Therefore, the correct answer is option B.
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An integer m is said to be related to another integer n, if m is a multiple of n. Then, the relation isa)reflexive and symmetricb)reflexive and transitivec)symmetric and transitived)equivalence relationCorrect answer is option 'B'. Can you explain this answer?
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