Answer
See explanation
Work Step by Step
We are asked to prove:
\[
\textbf{5. For all } a, b \in B,\quad (a \cdot b) + a = a
\]
---
### ✅ Proof:
Let \(a, b \in B\). We aim to show:
\[
(a \cdot b) + a = a
\]
---
### **Step 1**: Use the **Commutative Law** of +
\[
(a \cdot b) + a = a + (a \cdot b)
\]
---
### **Step 2**: Use the **Absorption Law**
From earlier exercises (Exercise 3), we already proved:
\[
a + (a \cdot b) = a
\]
---
### ✅ Final Answer:
\[
\boxed{(a \cdot b) + a = a}
\quad \text{(by commutativity and absorption law)}
\]
