Let$A = {0$, 1, 2, 3, 4, 5}. Let R be a relation$o_n$A defined by (x, y)$\ in $R if and only if max {x, y}$\ in ${3, 4}. Then among the statements (S ) : The number of elements\in \mathbb{R} is 18 , and (S ) : The relation R is symmetric but 1 2 neither reflexive nor transitive
Step-by-Step Solution
Key Concept: Translate the finite relation rule into explicit admissible ordered pairs and count the required set.
$A = {0$, 1, 2, 3, 4, 5} (3) R ≡ {(0, 3), (3, 0), (0, 4), (4, 0), (1, 3), (3, 1), (1, 4), (4, 1), (2, 3), (3, 2), (2, 4), (4, 2), (3, 3), (3, 4), (4, 3) , (4, 4)} Total 16 elements Not reflexive as (0, 0),$\ldots$$\ldots$, (2, 2) $\notin$ R Symmetric ∵ ∀ all a,b (a, b)&(b, a)$\ in $R Not transitive ∵ (0, 3), (3, 1)$\ in $R but (0, 1) $\notin$ R $\Rightarrow$ Only S correct 2
Correct Answer: 3