. Let F(X, Y, Z)=(X + Y + Z)(X + Y + Z)(X + Y + Z)(X + Y + Z). Use a 3-variable K-Map to find the minimized SOP form of this function. Hint: When you go to fill in the K-Map, you may have trouble figuring out where to put the 0s and 1s because F is specified in POS form. Your first impulse may be to try to multiply out these terms to convert it into SOP form, and then use that to fill in the K-Map. This would be logically correct but a ton of work. Instead you can use the POS form to determine where to place the 0s in the K-Map. For example, the first term (X+Y +Z) implies that you should put a zero in the square that corresponds to (X + Y + Z¯). Now use DeMorgan’s to see that (X + Y + Z¯) = X ·Y ·Z and place a 0 in the corresponding square. Repeat this for all the product terms; then you can fill in 1s in the squares without 0s.