The inclusion of which of the following sets into
$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $
is necessary and sufficient to make $S$ a complete lattice under the partial order defined by set containment?
- $\{1\}$
- $\{1\}, \{2, 3\}$
- $\{1\}, \{1, 3\}$
- $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$