Which of the following correctly applies De Morgan's law to ¬(A ∧ B)?
A¬A ∧ ¬B
B¬A ∨ B
C¬A ∨ ¬B
DA ∨ B
De Morgan's law states ¬(A ∧ B) = ¬A ∨ ¬B. Both things change simultaneously: the connective flips (AND → OR) AND complements are added to each variable. A common error is flipping only the complements but not the connective (leaving ¬A ∧ ¬B), or flipping only the connective without adding complements.
Question 2 True / False
In Boolean algebra, AND distributes over OR but OR does not distribute over AND — just like in ordinary arithmetic where multiplication distributes over addition but not vice versa.
TTrue
FFalse
Answer: False
In Boolean algebra, BOTH operations distribute over each other: A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C), and also A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C). This symmetric distributivity (the principle of duality) is one of the key structural differences from ordinary arithmetic, where only multiplication distributes over addition.
Question 3 Short Answer
What does it mean for a Boolean expression to be in Disjunctive Normal Form (DNF), and why is it useful?
Think about your answer, then reveal below.
Model answer: A Boolean expression is in DNF when it is written as an OR of AND-terms (minterms), where each AND-term contains only literals (variables or their complements). Every Boolean function has a DNF representation, making it a canonical form useful for verifying equivalences and constructing circuits directly from truth tables.
DNF corresponds directly to a truth table: each minterm covers exactly one row where the function outputs 1. This makes it easy to build any function from its truth table mechanically — one AND-term per true row — and provides a normal form for comparing whether two expressions are equivalent.