Question

Construct a truth table for the following function and from the truth table obtain an expression for the inverse function.

F2(A,B,C) = AC + BC + AB'

Answer 1

[A]	[B]	[C]	[F2 = AC+BC+AB']	[F2']
0	0	0	0	1
0	0	1	0	1
0	1	0	0	1
0	1	1	1	0
1	0	0	1	0
1	0	1	1	0
1	1	0	0	1
1	1	1	1	0

The inverse function is 1 for minterms [m₀​, m₁​, m_2​, m₆​]

Therefore,

F2′ ​= Σm(0, 1, 2, 6)

F2′ ​= A′B′C′ + A′B′C + A′BC′ + ABC′

On simplification,

F2′​ = A′B′ + BC′

Using De Morgan’s theorem, its POS form is:

F2′ ​= (AC + BC + AB′)′

F2′ ​= (A′ + C′)(B′ + C′)(A′ + B)