The area of the region consisting of points \( (x, y) \) satisfying \( |x \pm y| \leq 2 \) and \...

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The area of the region consisting of points \( (x, y) \) satisfying \( |x \pm y| \leq 2 \) and \( x^{2}+y^{2} \geq 2 \) is
(A) \( 8-2 \pi \) sq. units
(B) \( 4-2 \pi \) sq. units
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(C) \( 1-2 \pi \) sq. units
(D) \( 2 \pi \) sq. units
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