InterviewSolution
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InterviewSolution
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Show that the relation R in the set R of real numbers, defined as `R={(a ,b): alt=b^2}`is neither reflexive nor symmetric nor transitive. |
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Answer» `R={(a,b):a le b^(2)}` Here `(1,1) in R " as " 1 le 1, " but " 0.5 notin R " as " 0.5 gt (0.5)^(2)` Therefore, R is not reflexive. Now, `(1,4) in R " as " 1 lt 4^(2)` But, 4 is not less than 1. Therefore, `(4,1) notin R` Therefore, R is not symmetric. Further, `(3,2),(2,1.5) in R ("as "3 lt 2^(2) " and " 2 lt (1.5)^(2))` But, ` 3 gt (1.5)^(2)=2.25` Therefore, `(3,1.5) notin R` Therefore, R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive. |
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