Verified Solution • 2025–26 Session
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QJEEM20Ma4c00: JEE Main 2020 Mathematics - Class 11 JEEM20Ma4c00 Solution: If R = {(x, y) : x, y Z, x 2 + 3y 2 8} is a relation on the set …
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 :
Multiple Choice Options
- A {0, 1}
- B {–2, –1, 1, 2}
- C {–1, 0, 1}
- D {–2, –1, 0, 1, 2}
Step-by-Step Verified Solution
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}