Simplify the following Boolean function:

f (A, B,C) = \(\overline A BC\) + \(A\overline B C\) + \(AB\overline C \) + ABC

f (A, B,C) = \(\overline A BC\) + \(A\overline B C\) + \(AB\overline C \) + ABC

 \(\bar A BC + A\bar BC + AB(C+\bar C)\)

The above equation can also be written as :

= \(\bar ABC(A+\bar A) + A\bar BC( B+ \bar B)+ABC + AB\bar C\)

= \(0+ BC+AC+0+AB(C+\bar C)\)

= \(BC + AC+ AB\)

Hence option 3 is correct

Formulae:

1. A + 1 = 1
2. A + 0 = A
3. A . 1 = A
4. A . 0 = 0
5. A + A = A
6. A . A = A
7. \(\bar A\) = A
8. A + \(\bar A\) = 1
9. A . \(\bar A\) = 0
10. A+B = B+A
11. A.B = B.A
12. A+B = \(\bar A\).\(\bar B\)
13. A.B = \(\bar A\)+\(\bar B\)