Use a Karnaugh map to reduce each expression to a minimum SOP form:(a) A + B(overline C) + CD

Sure, let's simplify the given expression using a Karnaugh map.

The given expression is: A + B(overline C) + CD

Step 1: Draw a Karnaugh map

A Karnaugh map for three variables (A, B, C) looks like this:

      BC
      00 01 11 10
    -------------
A 0 |   |   |   |   |
    -------------
  1 |   |   |   |   |
    -------------

Step 2: Fill in the Karnaugh map

For the term A, fill in all cells in the row where A = 1.

For the term B(overline C), fill in the cells where B = 1 and C = 0.

For the term CD, fill in the cells where C = 1 and D = 1. But since D is not a variable in our map, we ignore this term.

The filled Karnaugh map looks like this:

      BC
      00 01 11 10
    -------------
A 0 |   |   |   |   |
    -------------
  1 | 1 | 1 | 1 | 1 |
    -------------

Step 3: Group the 1s

In a Karnaugh map, we group the 1s to simplify the expression. The groups should be as large as possible and can overlap. Each group represents a term in the simplified expression.

In this case, we can make one group of four 1s. This group represents the term A.

So, the simplified expression is: A

Therefore, the minimum SOP form of the given expression A + B(overline C) + CD is A.