To solve this question, the user needs to know the basics of Boolean algebra and simplification of Boolean functions using Boolean laws and rules.
Given Boolean function f = A.B.C.D + A.C.D + A.D
We can use Boolean algebraic manipulation to simplify the function as follows:
f = A.B.C.D + A.C.D + A.D
f = A.(B.C.D + C.D + D) //factor out A
f = A.(B.C.D + D.(C+1)) //factor out D
f = A.(B.C.D + D) //C+1=1
f = A.D.(B.C + 1) //factor out A.D
f = A.D //B.C+1=1
Therefore, the simplified Boolean function is f = A.D
Option A is the correct answer.
Option B is incorrect since B.C does not appear in the simplified function.
Option C is incorrect since the simplified function does not include A.B or C.
Option D is incorrect since the correct answer is A.
The Answer is: A. A.D