You have the Boolean expression:
$F = A'BC + AB'C + ABC' + ABC$

Let’s simplify this step-by-step.

Step 1: Group terms

We can group the terms based on common factors: $F = (A'BC) + (AB'C) + (ABC' + ABC)$

Step 2: Simplify the terms within parentheses

1. For the first two terms $(A'BC)$ and $(AB'C)$, there are no common factors, so we leave them as they are.

2. For the last two terms $(ABC' + ABC)$, we can factor out $AB$ from both terms: $ABC' + ABC = AB(C' + C)$ Now, using the Boolean identity $C' + C = 1$, we get: $AB(C' + C) = AB \cdot 1 = AB$

So, the expression simplifies to: $F = A'BC + AB'C + AB$

Step 3: Check for further simplifications

Now, we examine if we can simplify further:

• $A'BC$ and $AB'C$ have no common factors, so they remain unchanged.
• $AB'C$ and $AB$ do not share a common factor, so no further simplification can be made.

Thus, the simplified Boolean expression is: $F = A'BC + AB'C + AB$

Would you like me to explain any further steps or the reasoning behind the simplifications? Let me know!