) F(A,B,C,D)=Σm(1,2,5,6,8,9)

The given function F(A,B,C,D) = Σm(1,2,5,6,8,9) is a representation of a Boolean function in Sum of Products (SOP) form using minterms. The minterms (1,2,5,6,8,9) represent the decimal numbers where the function F is true.

Here's how you can write the function in terms of the variables A, B, C, and D:

1. Convert the minterm numbers to binary. Since we have 4 variables, we need 4 binary digits:

   1 = 0001, 2 = 0010, 5 = 0101, 6 = 0110, 8 = 1000, 9 = 1001

2. Write the minterms in terms of the variables. If a binary digit is 1, write the corresponding variable. If a binary digit is 0, write the corresponding variable with a bar over it (which means NOT).

   1 = A'B'C'D, 2 = A'B'CD', 5 = A'BC'D, 6 = A'BCD, 8 = AB'C'D', 9 = AB'C'D

3. Combine these minterms with OR operations to get the final function:

   F(A,B,C,D) = A'B'C'D + A'B'CD' + A'BC'D + A'BCD + AB'C'D' + AB'C'D

This is the expanded form of the given function using minterms.