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Question
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is ______.
Options
Reflexive and symmetric
Transitive and symmetric
Equivalence
Reflexive, transitive but not symmetric
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Solution
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is reflexive, transitive but not symmetric.
Explanation:
Since n divides n, ∀ n ∈ N, R is reflexive.
R is not symmetric since for 3, 6 ∈ N, 3 R 6 ≠ 6 R 3.
R is transitive since for n, m, r whenever n/m and m/r ⇒ n/r,
i.e., n divides m and m divides r, then n will devide r.
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