Let A={1,2,3} Define a relation R on A as aRb⇔a2−b2≤5then which of the following is/are true

R is reflexive and symmetric , R -1 = R (where R -1 is inverse of R) , R is symmetric and transitive

Let A={1,2,3} Define a relation R on A as aRb⇔a2−b2≤5then which of the following is/are true

A = { 1 , 2 , 3 } Define a relation R on A as aRb ⇔ a 2 − b 2 ≤ 5 R = { ( 1 , 1 ) ( 1 , 2 ) ( 2 , 2 ) ( 2 , 1 ) ( 2 , 3 ) ( 3 , 2 ) ( 3 , 3 ) } ( 3 , 2 ) ∈ R , ( 2 , 1 ) ∈ R but ( 3 , 1 ) ∉ R so not transitive

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Let $A = {1, 2, 3}$ Define a relation R on A as $aRb \Leftrightarrow |a^{2} - b^{2}| \leq 5$ then which of the following is/are true

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R is reflexive and symmetric

R^-1 = R (where R^-1 is inverse of R)

Range of R is A

R is symmetric and transitive

answer is A, B, D.

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Detailed Solution

$A = {1, 2, 3}$ Define a relation R on A as $aRb \Leftrightarrow |a^{2} - b^{2}| \leq 5$
$\begin{array}{l} R = {(1, 1) (1, 2) (2, 2) (2, 1) (2, 3) (3, 2) (3, 3)} \\ (3, 2) \in R, (2, 1) \in R but (3, 1) \notin R so not transitive \end{array}$