Consider the Boolean function of four variables: f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) The function is: (A) Independent of one variables(B) Independent of two variables(C) Independent of three variables(D) Dependent on all the variables

The function f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) is a Boolean function of four variables. To determine the dependency of the function on the variables, we need to write down the minterms represented by the given decimal numbers in the sum of minterms form.

The minterms are:

1 = 0001 (w'x'y'z) 3 = 0011 (w'x'y z) 4 = 0100 (w'x y'z) 6 = 0110 (w'x y z) 9 = 1001 (w x'y'z) 11 = 1011 (w x'y z) 12 = 1100 (w x y'z) 14 = 1110 (w x y z)

From the above minterms, we can see that:

• The variable 'w' appears in both its true and complemented form. Hence, the function is dependent on 'w'.
• The variable 'x' also appears in both its true and complemented form. Hence, the function is dependent on 'x'.
• The variable 'y' appears in both its true and complemented form. Hence, the function is dependent on 'y'.
• The variable 'z' appears only in its true form. Hence, the function is independent of 'z'.

So, the function is independent of one variable. Therefore, the correct answer is (A) Independent of one variable.