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

Question

Which of the following is not correct for relation R on the set of real numbers ? (A) ( x , y ) ∈ R Leftrightarrow 0<| x |-| y | ≤ 1 is neither transitive nor symmetric. (B) ( x , y ) ∈ R Leftrightarrow 0<| x - y | ≤ 1 is symmetric and transitive. (C) ( x , y ) ∈ R Leftrightarrow| x |-| y | ≤ 1 is reflexive but not symmetric. (D) ( x , y ) ∈ R Leftrightarrow| x - y | ≤ 1 is reflexive and symmetric.

Tardigrade Admin · Accepted Answer

Correct answer is (b) ( x , y ) ∈ R Leftrightarrow 0<| x - y | ≤ 1 is symmetric and transitive.

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

$(x, y) \in R \Leftrightarrow 0 < ∣ x ∣ - ∣ y ∣ \leq 1$ is neither transitive nor symmetric.

$(x, y) \in R \Leftrightarrow 0 < ∣ x - y ∣ \leq 1$ is symmetric and transitive.

$(x, y) \in R \Leftrightarrow ∣ x ∣ - ∣ y ∣ \leq 1$ is reflexive but not symmetric.

$(x, y) \in R \Leftrightarrow ∣ x - y ∣ \leq 1$ is reflexive and symmetric.

Correct answer is (b) $(x, y) \in R \Leftrightarrow 0 < ∣ x - y ∣ \leq 1$ is symmetric and transitive.

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

(x,y)∈R⇔0<∣x∣−∣y∣≤1 is neither transitive nor symmetric.

(x,y)∈R⇔0<∣x−y∣≤1 is symmetric and transitive.

(x,y)∈R⇔∣x∣−∣y∣≤1 is reflexive but not symmetric.

(x,y)∈R⇔∣x−y∣≤1 is reflexive and symmetric.