Textbook Problem

In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer.

Let $X=\left\{a,b,c\right\}$ and $P\left(X\right)$ be the power set of X. A relation L is defined on $P\left(X\right)$ as follows: For every A,B $A,B\in \left(X\right),A\text{L}B\iff$ the number of elements in A is less than the number of elements in B.