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1.Relation and Function
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Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is
A
Reflexive
B
Symmetric
C
Transitive
D
All of above
Solution
(d) Here ${l_1}R{l_2}$
${l_1}$ is parallel ${l_2}$ and also ${l_2}$ is parallel to ${l_1}$, so it is symmetric.
Clearly, it is also reflexive and transitive.
Hence it is equivalence relation.
Standard 12
Mathematics
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