1. Simplify the following logic expressions using algebraic manipulation:F ABCD BCD ACD

1. Break Down the Problem

To simplify the logic expression F = ABCD + BCD + ACD, we will analyze each component of the expression.

2. Relevant Concepts

We will use Boolean algebra rules, including:

• Idempotent Law: $A + A = A$
• Absorption Law: $A + AB = A$
• Distributive Law: $A(B + C) = AB + AC$

3. Analysis and Detail

Let’s simplify the expression step by step:

1. Start with the original expression: $F = ABCD + BCD + ACD$

2. Notice that the terms $BCD$ and $ACD$ share common factors. We can factor $CD$ out: $F = ABCD + CD(B + A)$

3. The term $B + A$ does not simplify further. Therefore: $F = CD(B + A) + ABCD$

4. However, $ABCD$ can be seen as part of $CD(B + A)$ since if both $A$ and $B$ are true, $CD$ will also be true. The term $ABCD$ is absorbed into $CD(B + A)$: $F = CD(B + A)$

4. Verify and Summarize

The simplification leads us to: $F = CD(B + A)$

This means $F$ can be expressed as a product of $CD$ and the sum $B + A$.

Final Answer

The simplified expression is: $F = CD(B + A)$