Question

The relation \( R \) defined on set \( A = \{x : |x|<3, x \in \mathbb{R} \} \) by \( R = \{(x, y): y = |x|\} \) is

• A. \( \{(2, 2), (1, 1), (0, 0), (1, 1), (2, 2)\} \)
• B. \( \{(2, -2), (-2, -2), (1, 1), (0, 0), (1, -2)\} \)
• C. \( \{(0, 0), (1, 1), (2, 2)\} \)
• D. None of the above

Hint:

In relations involving absolute values, both positive and negative values of \( x \) yield the same \( y \) value.

Answer 1

The Correct Option is A

Step 1: Identifying the relation.
The relation is defined as \( y = |x| \), so each element of the set \( A \) corresponds to the absolute value of \( x \). The correct set corresponds to option (1).

Step 2: Conclusion.
The correct answer is option (1).