[Math] Simplifying the Boolean expression $A’BC’ + AB’C + ABC’ + ABC$

Question

I have this Boolean to simplify.

$\bar AB\bar C + A\bar BC + AB\bar C + ABC$

I checked the final answer here. It gives the final simplification is $B\bar C + AC$

but I am confused here :

$\bar AB\bar C + A\bar BC + AB\bar C + ABC$

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

$\bar AB\bar C + A\bar BC + AB$

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

$\bar AB\bar C + A(C + B)$

$\bar AB\bar C + AC + AB$

$B(\bar A\bar C + A) + AC$ (1st and 3rd considered)

$B(\bar C + A) + AC$

$B\bar C + AB + AC$

Here, How can I go further to simplify $B\bar C + AB + AC$ to $B\bar C + AC$

How to remove $AB$ ?

Answer 1

I suggest you swap $AB'C$ and $ABC'$ before simplifying:

$$\begin{align}&A'BC' + ABC' + AB'C + ABC \\=& (A'+A)BC' + (B'+B)AC \\=& BC' + AC. \end{align}$$