Which of the following is not correct for relation R on the set of real numbers ?

Question

Accepted Answer

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 \le  |x -- y| = 0.7 \le  1

0 \le  |y -- z| = 0.6 \le  1

But |x -- z| = 1.3 > 1

So, (b) is correct.

Solutions · 1