I've solved my problem in this way:
1- i have to find prime implicants for minterms
ABC'=110X (where x indicates don't care values which is here D)
ACD'=1X10
A'B'D=00X1
B'CD=X011
A'C'D=0X01
then i've arranged them upstairs according to the number of 1's(just for arrangement):
00x1
0x01
x011
1x10
110x
I found p-implicants by combining pairs of them that can be combined so p-implicants are:
0xx1
x0x1
2- I have to find essential prime implicants as follows:
p-implicants minterms
00x1 0x01 x011 1x10 110x
0xx1 * *
x0x1 * *
the essential p-implicants are those who have single one in the column
so they are: 0xx1, x0x1
3- find the minimal subset of the remaining covering the uncovered with single one in a column, so we have one column that contains that subset and we should select on of the items in that column , let us choose the upper one (0xx1) , note: here's no matter whether to select the upper or the lower one causer they both will give use the same result as follows:
result=A'D+B'D+ A'D (or B'D)
Both will give us according to the property A+A=A :
result=A'D+B'D=(A'+B')D
I'm not sure yet of my solution there may be some errors, could you check it?!
thank a lot!
best regrads!