Sets Relations And Functions Question 60
Question: Let a relation R be defined by R = {(4, 5); (1, 4); (4, 6); (7, 6); (3, 7)} then $ {R^{-1}}oR $ is
Options:
A) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
B) {(1, 1), (4, 4), (7, 7), (3, 3)}
C) {(1, 5), (1, 6), (3, 6)}
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- We first find $ {R^{-1}}, $ we have $ {R^{-1}}={(5,,4);,(4,,1);,(6,,4);,(6,,7);,(7,,3)} $ . We now obtain the elements of $ {R^{-1}}oR $ we first pick the element of R and then of $ {R^{-1}} $ . Since $ (4,,5)\in R $ and $ (5,,4)\in {R^{-1}} $ , we have $ (4,,4)\in {R^{-1}}oR $ Similarly, $ (1,,4)\in R,,(4,,1)\in {R^{-1}}\Rightarrow ,(1,,1)\in {R^{-1}}oR $ $ (4,,6)\in R,,(6,,4)\in {R^{-1}}\Rightarrow ,(4,,4)\in {R^{-1}}oR, $ $ (4,,6)\in R,,(6,,7)\in {R^{-1}}\Rightarrow ,(4,,7)\in {R^{-1}}oR $ $ (7,,6)\in R,,(6,,4)\in {R^{-1}}\Rightarrow ,(7,,4)\in {R^{-1}}oR, $ $ (7,,6)\in R,,(6,,7)\in {R^{-1}}\Rightarrow ,(7,,7)\in {R^{-1}}oR $ $ (3,,7)\in R,,(7,,3)\in {R^{-1}}\Rightarrow ,(3,,3)\in {R^{-1}}oR, $ Hence, $ {R^{-1}}oR= $ {(1, 1); (4, 4); (4, 7); (7, 4), (7, 7); (3, 3)}.
BETA
