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Consider the following statements: 1. Parallelism of lines is an equivalence relation. 2. x R y, if x is a father of y, is an equivalence relation. Which of the statements given above is/are correct?A. 1 onlyB. 2 onlyC. Both 1 and 2D. Neither 1 nor 2 |
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Answer» Correct Answer - A Statement 1: Let l, m, n are parallel line and R is a relation. `therefore l||l`, then R is reflexive. and l||m and m||l, the R is symmetric. also l||m, m||n implies l||n, then R is transitive. Hence, R is an equivalence relation. Statement 2: x is father of y then x is not the father of x, so relation is not reflexive. Also, x is father of y but y is not father of x, so it is not symmetric. And x is father of y and y is father of z does not imply that x is father of z so, it is not transitive too. So, this is not an equivalence relation. so, only statement 1 is correct. |
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