4. Minimize the following Boolean functions into product-of-sums form using a K-map \text { (a) } \boldsymbol{F}(w, x, y, z)=\sum(0,2,3,4,7,8,11,13,15) \text { (b) } F(a, b, c, d)=\sum(0,2,4,5,8,9,10,15) \text {

(c) } F\left(w, x_{2} y, z\right)=\prod(2,4,5,8,9,10,11,14,15) \text { (d) } F(a, b, c, d)=\prod(1,2,4,5,8,9,10,11,12)