Problem $4.(15$ points$)$:

Reduce the following Boolean expressions to a minimum number of terms using a Karnaugh map:

$Y\frac{?}{b}=ar(A)\frac{*}{b}ar(B)\frac{*}{b}ar(C)\frac{*}{b}ar(D)+A\frac{*}{b}ar(B)\frac{*}{b}ar(C)+A\frac{*}{b}ar(B)*C\frac{*}{b}ar(D)+A*B*D\frac{+}{b}ar(A)\frac{*}{b}ar(B)*C\frac{*}{b}ar(D)+B\frac{*}{b}ar(C)*D\frac{+}{b}ar(A)$