Sets, Relations & Functions
Sets and Relations
nta_pyq_2025_jan
Grade 11
Question:
Let A = {(x, y) \in R \times R : |x + y| \ge 3} and B = {(x, y) \in R \times R : |x| + |y| \le 3}. If C = {(x, y) \in A \cap B : x = 0 or y = 0}, then \sum (x,y)\inC |x + y| is :
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
A = {(x, y) \in R \times R : |x + y| \ge 3} (4) and B = {(x, y) \in R \times R : |x| + |y| \le 3} C = {(x, y) \in A \cap B : x = 0 or y = 0} A \cap B will have only common points lying on the line P Q and RS Now, C = {(-3, 0), (3, 0), (0, 3), (0, -3)} \sum |x + y| = 3 + 3 + 3 + 3 = 12 (x,y)\inc y
Correct Answer: 4