Let and If , then is: [2025]

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Solution

Q.
Let $A = {(x, y) \in R \times R : | x + y | \geq 3}$ and $B = {(x, y) \in R \times R : | x | + | y | \leq 3}$

If $C = {(x, y) \in A \cap B : x = 0 or y = 0}$ , then $\sum_{(x, y) \in C}$ $| x + y |$ is: [2025]

1 18

2 12

3 24

4 15

Ans.
(2)

We have, $A = {(x, y) \in R \times R : | x + y | \geq 3}$ and $B = {(x, y) \in R \times R : | x | + | y | \leq 3}$

From given figure, we get C = {(3, 0), (–3, 0), (0, 3), (0, –3)}

$\sum_{(x, y) \in C} | x + y | = 12$

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