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$A=\{1,2,3,4,5\}, S=\{(x, y): x \in A, y \in A\}$, then find the ordered which satisfy the conditions given below,
(i) $x+y=5$
(ii) $x+y < 5$
(iii) $x+y>8$
(i) $x+y=5$
(ii) $x+y < 5$
(iii) $x+y>8$
Solution:
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Given $A=\{1,2,3,4,5\}$ and $S=\{x, y): x \in A, \in A\}$
(i) The ordered pairs satisfying $x+y=5$ is, $\{(1,4),(2,3),(3,2),(4,1)\}$.
(ii) The ordered pairs satisfying $x+y < 5$ is $\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)$.
(iii) The ordered pairs satisfying $x+y>8$ is $\{4,5),(5,4),(5,5)\}$
(i) The ordered pairs satisfying $x+y=5$ is, $\{(1,4),(2,3),(3,2),(4,1)\}$.
(ii) The ordered pairs satisfying $x+y < 5$ is $\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)$.
(iii) The ordered pairs satisfying $x+y>8$ is $\{4,5),(5,4),(5,5)\}$
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