Question
The relation $$R$$ defined on the set $$A = \left\{ {1,\,2,\,3,\,4,\,5} \right\}$$ by $$R = \left\{ {\left( {x,\,y} \right):\left| {{x^2} - {y^2}} \right| < 16} \right\}$$ is given by :
A.
$$\left\{ {\left( {1,\,1} \right),\,\left( {2,\,1} \right),\,\left( {3,\,1} \right),\,\left( {4,\,1} \right),\,\left( {2,\,3} \right)} \right\}$$
B.
$$\left\{ {\left( {2,\,2} \right),\,\left( {3,\,2} \right),\,\left( {4,\,2} \right),\,\left( {2,\,4} \right)} \right\}$$
C.
$$\left\{ {\left( {3,\,3} \right),\,\left( {3,\,4} \right),\,\left( {5,\,4} \right),\,\left( {4,\,3} \right),\,\left( {3,\,1} \right)} \right\}$$
D.
None of these
Answer :
None of these
Solution :
Here $$R = \left\{ {\left( {x,\,y} \right):\left| {{x^2} - {y^2}} \right| < 16} \right\}$$ and given $$A = \left\{ {1,\,2,\,3,\,4,\,5} \right\}$$
$$\therefore \,R = \left\{ {\left( {1,\,2} \right)\left( {1,\,3} \right)\left( {1,\,4} \right);\,\left( {2,\,1} \right)\left( {2,\,2} \right)\left( {2,\,3} \right)\left( {2,\,4} \right);\left( {3,\,1} \right);\left( {3,\,2} \right)\left( {3,\,3} \right)\left( {3,\,4} \right);\left( {4,\,1} \right)\left( {4,\,2} \right)\left( {4,\,3} \right);\left( {4,\,4} \right),\left( {4,\,5} \right),\left( {5,\,4} \right)\left( {5,\,5} \right)} \right\}$$