JEE Main 2020 — Sets And Relations Question with Solution
From: JEE Main 2020 (Online) 2nd September Morning Slot
Question
If R = {(x, y) : x, y
Z, x2 + 3y2
8} is a relation
on the set of integers Z, then the domain of R–1 is :
Choose an option
Show full solutionCorrect option: C
Correct answer
C{–1, 0, 1}
Step-by-step explanation
Given R = {(x, y) : x, y
Z, x2 + 3y2
8}
So R = {(0,1), (0,–1), (1,0), (–1,0), (1,1), (1,-1)
(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}
R : { -2, -1, 0, 1, 2} {-1, 0, 1}
R-1 : {-1, 0, 1} { -2, -1, 0, 1, 2}
Domain of R–1 = {-1, 0, 1}
So R = {(0,1), (0,–1), (1,0), (–1,0), (1,1), (1,-1)
(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}
R : { -2, -1, 0, 1, 2} {-1, 0, 1}
R-1 : {-1, 0, 1} { -2, -1, 0, 1, 2}
Domain of R–1 = {-1, 0, 1}
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