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Set 10: Linear Inequalities (Advanced)

Explanation

Answer: A

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

✓ Correct
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

Detailed Explanation

Choice A is correct. 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.

Key Steps:

The correct answer is x>2|x| > 2 or y>2|y| > 2

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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