3
algebra

Which inequality describes the region OUTSIDE the square with vertices (±2,±2)(\pm 2, \pm 2)?

A

x>2|x| > 2 or y>2|y| > 2

B

x>2|x| > 2 and y>2|y| > 2

C

x+y>2|x| + |y| > 2

D

x2+y2>4x^2 + y^2 > 4

Correct Answer: A

Choice A is the correct answer. De Morgan's Laws applied to geometry.

  1. Inside Square: x2|x| \leq 2 AND y2|y| \leq 2.
  2. Outside (Negation): NOT (x2|x| \leq 2 AND y2|y| \leq 2).
  3. Apply Logic: (NOT x2|x| \leq 2) OR (NOT y2|y| \leq 2).
  4. Result: x>2|x| > 2 OR y>2|y| > 2.

?�� Strategic Tip: The negation of "A and B" is "Not A or Not B".

Choice B is incorrect because it describes the corner regions only (diagonal from corners). Choice C is incorrect because it describes the region outside a diamond. Choice D is incorrect because it describes the region outside a circle.