CUET · MATHS · PYQ PAPER 2023
For real numbers x and y, the relation R is defined as R = {(x, y) : x + y - \(\pi\) is an irrational number}, then the relation R is:
- A reflexive
- B symmetric
- C transitive
- D equivalence
Answer & Solution
Correct Answer
(B) symmetric
Step-by-step Solution
Detailed explanation
If \( (x,x) \in R \), then \( x + x - \pi = 2x - \pi \) must be irrational. Let \( x = \frac{\pi}{2} \). Then \( 2(\frac{\pi}{2}) - \pi = 0 \), which is rational. Thus, R is not reflexive. If \( (x,y) \in R \), then \( x + y - \pi \) is irrational. Then…
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