Let begin mathsize 12px style R equals open curly brackets open parentheses 1 comma 3 close parentheses comma open parentheses 2 comma 2 close parentheses comma open parentheses 3 comma 2 close parentheses close curly brackets space a n d space S equals open curly brackets open parentheses 2 comma 1 close parentheses comma open parentheses 3 comma 2 close parentheses comma open parentheses 2 comma 3 close parentheses close curly brackets space b e space t w o space r e l a t i o n s space o n space s e t space A equals open curly brackets 1 comma 2 comma 3 close curly brackets. T h e n space R o S equals
i. open curly brackets open parentheses 1 comma 3 close parentheses comma open parentheses 2 comma 2 close parentheses comma open parentheses 3 comma 2 close parentheses comma open parentheses 2 comma 1 close parentheses comma open parentheses 2 comma 3 close parentheses close curly brackets space space space i i. open curly brackets open parentheses 3 comma 2 close parentheses comma open parentheses 1 comma 3 close parentheses close curly brackets space space space i i i. open curly brackets open parentheses 2 comma 3 close parentheses comma open parentheses 3 comma 2 close parentheses comma open parentheses 2 comma 2 close parentheses close curly brackets space space space i v. open curly brackets open parentheses 2 comma 3 close parentheses comma open parentheses 3 comma 2 close parentheses close curly brackets end style

Asked by sunil2791 | 17th Jun, 2017, 12:19: PM

Expert Answer:

begin mathsize 16px style straight R open parentheses 2 comma 2 close parentheses equals open curly brackets open parentheses 1 comma 3 close parentheses comma open parentheses 2 comma 2 close parentheses comma open parentheses 3 comma 2 close parentheses close curly brackets
rightwards double arrow straight R open parentheses 1 close parentheses equals 3 comma space straight R open parentheses 2 close parentheses equals 2 comma space straight R open parentheses 3 close parentheses equals 2........... left parenthesis straight i right parenthesis
straight S equals open curly brackets open parentheses 2 comma 1 close parentheses comma open parentheses 3 comma 2 close parentheses comma open parentheses 2 comma 3 close parentheses close curly brackets
rightwards double arrow straight S open parentheses 2 close parentheses equals 1 comma straight S open parentheses 3 close parentheses equals 2 comma straight S open parentheses 2 close parentheses equals 3............ left parenthesis ii right parenthesis
On space straight A equals open curly brackets 1 comma 2 comma 3 close curly brackets
rightwards double arrow straight R open square brackets straight S open parentheses 1 close parentheses close square brackets space where space straight S open parentheses 1 close parentheses space is space not space defined space here.
rightwards double arrow straight R open square brackets straight S open parentheses 2 close parentheses close square brackets equals straight R open parentheses 1 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis close parentheses
space space space space space space space space space space space space space space space space equals 3
rightwards double arrow open parentheses 2 comma 3 close parentheses
Simlilarly space
straight R open square brackets straight S open parentheses 2 close parentheses close square brackets equals straight R open parentheses 3 close parentheses.............. from space left parenthesis ii right parenthesis space we space have space two space values space of space straight S left parenthesis 2 right parenthesis
space space space space space space space space space space space space equals 2
rightwards double arrow open parentheses 2 comma 2 close parentheses
straight R open square brackets straight S open parentheses 3 close parentheses close square brackets equals straight R open parentheses 2 close parentheses equals 2
rightwards double arrow open parentheses 3 comma 2 close parentheses
Option space left parenthesis iii right parenthesis space is space correct space open curly brackets open parentheses 2 comma 3 close parentheses comma open parentheses 2 comma 2 close parentheses comma open parentheses 3 comma 2 close parentheses close curly brackets
end style

Answered by Sneha shidid | 19th Jun, 2017, 11:12: AM