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01/02/2022 1:50 pm
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Which of the following is not correct for relation R on the set of real numbers?
(1) (x, y) ∈ R ⇿ 0 < |x| - |y| ≤ 1 is neither transitive nor symmetric.
(2) (x, y) ∈ R ⇿ 0 < |x - y| ≤ 1 is symmetric and transitive.
(3) (x, y) ∈ R ⇿ 0 < |x| - |y| ≤ 1 is reflexive but not symmetric.
(4)(x, y) ∈ R ⇿ 0 < |x - y| ≤ 1 is reflexive and symmetric.
1 Answer
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01/02/2022 1:52 pm
Correct answer: (2) (x, y) ∈ R ⇿ 0 < |x - y| ≤ 1 is symmetric and transitive.
Explanation:
Note that (1, 2) and (2, 3) satisfy 0 < |x – y| ≤ 1 but (1,3) does not satisfy it so 0 ≤ |x – y| ≤ 1 is symmetric but not transitive.