GO Classes DPP | GATE CS | Digital Logic | Boolean Laws

Answer 1

Given:

$F=(A+\overline{B})(A+C)+\overline{A}B+BC$

Use the law $(X+Y)(X+Z)=X+YZ$.

Here, $X=A$, $Y=\overline{B}$, and $Z=C$.

So,

$(A+\overline{B})(A+C)=A+\overline{B}C$

Now substitute this back.

$F=A+\overline{B}C+\overline{A}B+BC$

Now use the law $A+\overline{A}B=A+B$.

So,

$F=A+B+\overline{B}C+BC$

Now combine $B+\overline{B}C$.

Using $X+\overline{X}Y=X+Y$,

$B+\overline{B}C=B+C$

Therefore,

$\boxed{F=A+B+C}$

Answer: A

Answer 2

Here is the explanationOr if you don't want a kmap then A+C+A'B → A+A'B+C →(A+A')(A+B)+C →A+B+C

Answer 3

Option A