A Level Computer Science OCR Practice Exam

What is the main purpose of De Morgan's Law in boolean algebra?

1. To simplify complex equations

2. To switch AND and OR operations

3. To provide equivalence rules

4. To negate variables

The correct answer is: To provide equivalence rules

De Morgan's Law is essential in Boolean algebra as it provides rules for transforming expressions involving logical operations. Specifically, it outlines a method for expressing the negation of a conjunction (AND operation) and the negation of a disjunction (OR operation) in terms of the other operation. These equivalences state that the negation of an AND operation is equivalent to the OR operation of the negated components, and conversely, the negation of an OR operation is equivalent to the AND operation of the negated components. This law is fundamental for simplifying complex logical expressions, facilitating circuit design, and proving various properties in digital logic. While simplifying complex equations is an important application, the primary purpose directly relates to establishing equivalence rules, thus allowing for consistent transformation and manipulation of logical statements. The option concerning switching AND and OR operations captures a specific application of De Morgan's Law, but it does not encompass its broader role in providing equivalence rules across all Boolean algebra expressions. Negating variables is also a partial aspect of how negation works within the context of De Morgan's Law, but again, it is not the main purpose of the law itself.