You copied the title wrong. The condition (1) is that both the empty set and the complete set u should be selected, and everything else should be copied correctly.

Solution: U = {a, b, c, d} * * has 16 subsets (omitted). In addition to the empty set and the complete set u, find two subsets at will.

{a} and {AB}, {AC}, {AD}, {ABC}, {Abd}, {ACD}. Six kinds.

{b} and {ab} {BC}, {BD}, {ABC}, {Abd}, {BCD}.

{c} and {AC}, {BC}, {CD}, {ABC}, {ACD} and {BCD}.

{d} and {ad}, {BD}, {CD}, {Abd}, {ACD}, {BCD}

{ab} and {abc}, {abd}. Two kinds.

{ac} and {abc}, {acd}.

{ad} and {adb}, {adc}.

{bc} and {abc}, {bcd}.

{bd} and {abd}, {cbd}.

There are {cd} and {ACD} and {BCD}, so there are ***36 kinds.