If {B, +,., 0, 1} is a Boolean algebra, then a+1=

(i) 1

(ii) 0

(iii) a

(iv) None of these

In Boolean algebra, one of the fundamental properties is:

\[ a + 1 = 1 \]

This is known as the **"absorption law"** in Boolean algebra. According to this law, the disjunction (OR) of any Boolean variable \(a\) with 1 will always result in 1, regardless of the value of \(a\).

Thus, the correct answer is:

**(i) 1**

Would you like further details or clarification on Boolean algebra? Here are 5 related questions to consider:

1. What is the absorption law in Boolean algebra?
2. How does the identity element for addition work in Boolean algebra?
3. What is the result of \(a \cdot 0\) in Boolean algebra?
4. Can you explain the duality principle in Boolean algebra?
5. How does Boolean algebra differ from standard algebra?

**Tip:** In Boolean algebra, the element 1 acts as the "true" value, and adding 1 to any Boolean variable always results in 1.

If {B, +, ., 0, 1} is a Boolean algebra, then a+1=
(i) 1
(ii) 0
(iii) a
(iv) None of these

Solve the Boolean algebra problem: If {B, +, ., 0, 1} is a Boolean algebra, what is a + 1? This problem explores the absorption law and disjunction (OR) operation in Boolean algebra, providing an explanation and step-by-step solution. Suitable for high school students in Grades 9-12.

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