The function AB’C + A’BC + ABC’ + A’B’C + AB’C’ is equivalent to
2004
The function
AB’C + A’BC + ABC’ + A’B’C + AB’C’
is equivalent to
- A.
AC’+AB+A’C
- B.
AB’+AC’+A’C
- C.
A’B+AC’+AB’
- D.
A’B+AC+AB’
Attempted by 47 students.
Show answer & explanation
Correct answer: B
Start with the given expression: AB' C + A' B C + A B C' + A' B' C + A B' C'
Combine the two terms with C': A B C' + A B' C' = A C'(B + B') = A C'.
Factor C from the three terms with C: A B' C + A' B C + A' B' C = C(AB' + A'B + A'B')
Simplify inside the parenthesis: AB' + A'B + A'B' = AB' + A'(B + B') = AB' + A' = A' + AB' = A' + B'.
So the C-group becomes C(A' + B') = A' C + B' C.
Putting the pieces together: A C' + A' C + B' C.
Show equivalence to the target form: B' C = A B' C + A' B' C, which is covered by A B' + A' C when combined with the other terms. Also A B' = A B' C + A B' C', covered by B' C + A C'. Therefore A C' + A' C + B' C is equivalent to A B' + A C' + A' C.
Final simplified expression: AB' + AC' + A'C