Let A = {(x, y) ∈ R x R : |x+y| ≥ 3} and B = {(x, y) ∈ R x R : |x| + |y| ≥ 3}.

Question

Let \(A=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geq 3\}\) and \(B=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}.\) If \(\mathrm{C}=\{(\mathrm{x}, \mathrm{y}) \in \mathbf{A} \cap \mathbf{B}: \mathrm{x}=0\) or \(\mathrm{y}=0\},\) then \(\sum_{(x, y) \in C}|x+y|\) is :

(1) 15

(2) 18

(3) 24

(4) 12

Answer 1

Correct option is (4) 12  

C = {(3, 0), (-3, 0), (0, 3), (0, -3)}

\(\Sigma|x+y|=12\)