A Level Computer Science OCR Practice Exam

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De Morgan's Law states that which of the following is true?

¬(X AND Y) ≡ ¬X AND ¬Y
¬(X OR Y) ≡ ¬X OR ¬Y
¬(X OR Y) ≡ ¬X AND ¬Y
¬(X AND Y) ≡ ¬X OR ¬Y

The correct answer is: ¬(X OR Y) ≡ ¬X AND ¬Y

The correct application of De Morgan's Law is found in the statement that negating a disjunction (X OR Y) means that both X and Y must be false. This translates mathematically to saying that the negation of the entire expression is equivalent to the conjunction of the negations of the individual expressions. Therefore, the statement ¬(X OR Y) ≡ ¬X AND ¬Y accurately represents one of De Morgan's Laws. This law is essential in logic and digital design, as it allows for the simplification of expressions and is foundational in creating equivalent logical statements. In contrast, the other statements misrepresent the relationships set forth by De Morgan's Laws, demonstrating misunderstandings of how negation interacts with conjunction and disjunction.