Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

The following is the incomplete operation table of a 4-element group. The last row of the table is

The inclusion of which of the following sets into

S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4},
{1, 2, 3, 4, 5} }
Is necessary and sufficient to make S a complete lattice under the partial order defined by set containment?

The binary relation $$S = \phi $$ (emply set) on set A = {1, 2, 3} is