JEE Mains · Maths · STD 12 - 1. relation and function
The probability that a relation \(R\) from \(\{ x , y \}\) to \(\{ x , y \}\) is both symmetric and transitive, is equal to
- A \(\frac{5}{16}\)
- B \(\frac{9}{16}\)
- C \(\frac{11}{16}\)
- D \(\frac{13}{16}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{16}\)
Step-by-step Solution
Detailed explanation
Total no. of relations \(=2^{2 \times 2}=16\) Fav. relation \(=\phi,\{( x , x )\},\{( y , y )\},\{( x , x )( y , y )\}\) \(\{(x, x),(y, y),(x, y)(y, x)\}\) Prob. \(=\frac{5}{16}\)
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