Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation R = { ( x , y ) A A : x + y = 7 } is [2023]

Question

Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation $R = {(x, y) \in A \times A : x + y = 7}$ is [2023]

Smart Achievers · Accepted Answer

(4)

Given, $A = {1, 2, 3, 4, 5, 6, 7}$

and $R = {(x, y) \in A \times A : x + y = 7}$

For Reflexive: Let $y = x$

So, $x + x = 7 \Rightarrow x = \frac{7}{2}$ , which is not possible.

So, the given relation is not reflexive.

For Symmetric: $x R y \Rightarrow x + y = 7$

$\Rightarrow$ $y + x = 7$ $∴$ $x R y \Rightarrow y R x$

Hence, the given relation is symmetric.

For Transitive: Let $x R y$ and $y R z \Rightarrow x + y = 7$ and $y + z = 7$ .

But it does not imply that $x + z = 7$ .

So, $R$ is not transitive.

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