The Sum of Products (SOP) form for the Boolean expression F(x, y, z)=1 is the canonical representation where the function outputs 1 for all possible minterms (combinations of the input variables x, y, z).
Since F(x, y, z)=1 for all inputs, the SOP form will include all the minterms of the 3 variables: F(x, y, z)= ∑(0, 1, 2, 3, 4, 5, 6, 7 )
The explicit SOP expression is: F(x, y, z) = x‾y‾z‾ + x‾y‾z + x‾yz‾ + x‾yz + xy‾z‾ + xy‾z + xyz‾ + xyz
Here: