Question
Let A be the set of all points in a plane and let O be the origin. Show that the relation and is an equivalence relation.
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Text solutionVerified
Let be the origin and
let be any three points in a plane.
Then,
(i) is always true. So, R is reflexive.
(ii) . So, R is symmetric.
(iii) . So, R transitive.
Hence, R is an equivalence relation.
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Question Text | Let A be the set of all points in a plane and let O be the origin. Show that the relation and is an equivalence relation. |
Answer Type | Text solution:1 |
Upvotes | 150 |