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Question: The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : \(\left. \left| x ^ { 2 } - ...

The relation R defined on the set A = {1, 2, 3, 4, 5} by

R = {(x, y) : ∣x2−y2∣<16}\left. \left| x ^ { 2 } - y ^ { 2 } \right| < 16 \right\} is given by

A

{(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}

B

{(2, 2), (3, 2), (4, 2), (2, 4)}

C

{(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)}

D

None of these

Answer

None of these

Explanation

Solution

Here R={(x,y):∣x2−y2∣<16}R = \left\{ ( x , y ) : \left| x ^ { 2 } - y ^ { 2 } \right| < 16 \right\}and given

A={1,2,3,4,5}A = \{ 1,2,3,4,5 \}

∴R={(1,2)(1,3)(1,4);(2,1)(2,2)(2,3)(2,4);(3,1)(3,2)R = \{ ( 1,2 ) ( 1,3 ) ( 1,4 ) ; ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ; ( 3,1 ) ( 3,2 )

(3,3)(3,4);(4,1)(4,2)(4,3);(4,4)(4,5),(5,4)(5,5)}( 3,3 ) ( 3,4 ) ; ( 4,1 ) ( 4,2 ) ( 4,3 ) ; ( 4,4 ) ( 4,5 ) , ( 5,4 ) ( 5,5 ) \}.