Question

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

F1(A,B,C) = A + BC'

Answer 1

[A]	[B]	[C]	[F1=A+BC']	[F1']
0	0	0	0	1
0	0	1	0	1
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	1	0
1	1	0	1	0
1	1	1	1	0

The inverse function is 1 for minterms [m₀, m₁, m₃]

Therefore,

F1′​ = Σm(0, 1, 3)

F1′ ​= A′B′C′ + A′B′C + A′BC

On simplification,

F1′ ​ =A′(B′ + C)

This also follows directly by De Morgan’s theorem:

F1′ ​= (A + BC′)′ = A′(B′ + C)