The relation R defined in A = 1,2,3 by aRb, if | a 2- b 2| ≤ 5. Which of the following is false?

Question

The relation R defined in A = 1,2,3 by aRb, if | a 2- b 2| ≤ 5. Which of the following is false? (A) R = (1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)  (B) R -1= R (C) Domain of R = 1,2,3  (D) Range of R= 5

Tardigrade Admin · Accepted Answer

R = (1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3) R -1= ( y , x ):( x , y ) ∈ R = (1,1),(2,1),(1,2),(2,2),(3,2),(2,3),(3,3) = R Domain of R = x :( x , y ) ∈ R = 1,2,3 Range of R = y :( x , y ) ∈ R = 1,2,3

Q. The relation $R$ defined in $A = {1, 2, 3}$ by $a R b$ , if $∣ ∣ a^{2} - b^{2} ∣ ∣ \leq 5$ . Which of the following is false?

$R = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)}$

$R^{- 1} = R$

Domain of $R = {1, 2, 3}$

Range of $R = {5}$

$R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3)}$
$R^{- 1} = {(y, x) : (x, y) \in R}$
$= {(1, 1), (2, 1), (1, 2), (2, 2), (3, 2), (2, 3), (3, 3)} = R$
Domain of $R = {x : (x, y) \in R} = {1, 2, 3}$
Range of $R = {y : (x, y) \in R} = {1, 2, 3}$

Q. The relation R defined in A={1,2,3} by aRb, if ∣∣​a2−b2∣∣​≤5. Which of the following is false?

R={(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)}

R−1=R

Domain of R={1,2,3}

Range of R={5}