The number of relations$o_n$the set$A = {1$, 2, 3} containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is ________
Step-by-Step Solution
Key Concept: Translate the finite relation rule into explicit admissible ordered pairs and count the required set.
$A = {1$, 2, 3} (1, 1), (2, 2), (3, 3), (1, 2)$\ in $R (5) Remaining elements are (2, 1), (2, 3), (1, 3), (3, 1), (3, 2) (1) If relation contains exactly 4$elements = 1$way (2) if relation contains exactly 5 elements It can be (1, 3), (3, 2) $\Rightarrow$ 2 ways (3) If relation contain exactly 6 elements It can be ((2, 3), (1, 3)), ((1, 3), (3, 2)), ((3, 1), (3, 2)) $\Rightarrow$ 3 ways.$Total = 6$ways
Correct Answer: 5