Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X, and Y ∩ Z is empty is:

Y ⊆ X, Z ⊆ X
Let a ∈ X, then
a ∈ Y, a ∈ Z (1)
a ∉ Y, a ∈ Z (2)
a ∈ Y, a ∉ Z (3)
a ∉ Y, a ∉ Z (4)
We require Y ∩ Z = φ
Thus, for a, equation (1), (2) and (3) can satisfy Y ∩ Z = φ
Therefore, Y ∩ Z = φ has 3 options.
Thus, No. of required possibilities for 5 elements of X = 35 = 243