JEE MAIN - Mathematics (2021 - 31st August Morning Shift - No. 6)
Which of the following is not correct for relation R on the set of real numbers ?
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.
Explanation
Note that (a, b) and (b, c) satisfy 0 < |x $$-$$ y| $$\le$$ 1 but (a, c) does not satisfy it so 0 $$\le$$ |x $$-$$ y| $$\le$$ 1 is symmetric but not transitive.
For example,
x = 0.2, y = 0.9, z = 1.5
0 ≤ |x – y| = 0.7 ≤ 1
0 ≤ |y – z| = 0.6 ≤ 1
But |x – z| = 1.3 > 1
So, (b) is correct.
For example,
x = 0.2, y = 0.9, z = 1.5
0 ≤ |x – y| = 0.7 ≤ 1
0 ≤ |y – z| = 0.6 ≤ 1
But |x – z| = 1.3 > 1
So, (b) is correct.
Comments (0)
