If R be a relation < from A = {1,2, 3, 4} to B = {1, 3, 5} i.e., (a,,b) ∈ R Leftrightarrow a &l

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1.Relation and Function

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If $R$ be a relation $<$ from $A = \{1,2, 3, 4\}$ to $B = \{1, 3, 5\}$ i.e., $(a,\,b) \in R \Leftrightarrow a < b,$ then $Ro{R^{ - 1}}$ is

A

$\{(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)\}$

B

$\{(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)\}$

C

$\{(3, 3), (3, 5), (5, 3), (5, 5)\}$

D

$\{(3, 3) (3, 4), (4, 5)\}$

Solution

(c) We have, $R = \{(1, 3); (1, 5); (2, 3); (2, 5); (3, 5); (4, 5)\}$

${R^{ – 1}} = \{(3, 1), (5, 1), (3, 2), (5, 2); (5, 3); (5, 4)\}$

Hence $Ro{R^{ – 1}}= \{(3, 3); (3, 5); (5, 3); (5, 5)\}.$

Standard 12

Mathematics

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