Let X = \ 1, 2, 3, 4\ and P(X) be the power set of X . A relation R...

For reflexivity:
For any set $A \in P(X)$, we know that $A \subseteq A$.
Thus, the condition $A \subseteq A$ or $A \subseteq A$ is satisfied, which means $A \, R \, A$.
So, $R$ is reflexive.

For symmetry:
If $A \, R \, B$, then $A \subseteq B$ or $B \subseteq A$.
This logically implies $B \subseteq A$ or $A \subseteq B$, which means $B \, R \, A$.
So, $R$ is symmetric.

For transitivity:
Let $A = \{1\}$, $B = \{1, 2\}$, and $C = \{2\}$.
Here, $A \subseteq B$, so $A \, R \, B$ holds.
Also, $C \subseteq B$, which means $B \, R \, C$ holds.
However, neither $A \subseteq C$ nor $C \subseteq A$ is true, so $A$ is not related to $C$.
So, $R$ is not transitive.

Therefore, the relation $R$ is reflexive and symmetric only.

Answer: reflexive and symmetric only