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Question #40310

Difficulty: 8/10 | 🟢 Free

The Question

Let $A = \{x \in \mathbb{R} : ||x-2| - 1| \ge 3 \}$ and $B = \left\{x \in \mathbb{R} : \frac{|x+1| - 2}{|x-3| - 1} \le 0 \right\}$ . If $S = (A \Delta B)^c$ , where $A \Delta B$ denotes the symmetric difference of sets $A$ and $B$ , find the sum of all integers in $S$ .

Options

A.
0
B.
4
C.
6
D.
11

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Difference vs. Symmetric Difference|Modulus Inequality Logic|Modulus Function Breakdown

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to systematically solve nested and rational modulus inequalities, and perform complex set operations on the resulting intervals.

The primary trap lies in the rational modulus inequality for set B: students frequently forget that the denominator cannot be zero, incorrectly including the boundary points x=2 and x=4.

This boundary inclusion error propagates through the symmetric difference operation, altering the final set of integers.

Furthermore, calculating the complement of a symmetric difference requires precise interval algebra, punishing students who rely on intuition rather than rigorous number-line partitioning.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Sets - Class 11
Concept	Difference vs. Symmetric Difference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free