Let P be the set of all subsets of \(\{1, 2, 3\}\), and let R be the relation on P defined by \(R = \{(X, Y) : X \subseteq Y\}\). Then R is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → reflexive and transitive but not symmetric
Reflexive: every set is a subset of itself, so \(X \subseteq X\) for every X in P.
Symmetric fails:
\(\{1\} \subseteq \{1, 2\}\), but \(\{1, 2\} \not\subseteq \{1\}\)
Transitive: if \(X \subseteq Y\) and \(Y \subseteq Z\), then every element of X is in Y, and so in Z. Hence \(X \subseteq Z\).
So R is reflexive and transitive but not symmetric.