Question

Which of the following is correct regarding the conversion of boolean expressions?

a) CNF can always be converted to DNF, but the reverse may not be true.
b) DNF can always be converted to CNF, but the reverse may not be true.
c) Both CNF and DNF can be converted to each other interchangeably.
d) CNF and DNF cannot be converted to each other.

Answer 1

The correct answer is that both CNF and DNF can be converted to each other interchangeably. However, for algebraic equations involving factorization, we can only conclude A = B if F is not zero in examples where A and B are multiplied or divided by F.

Step-by-step explanation:

The question revolves around the concept of boolean expression conversion and understanding the relationship between Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF). Answering the multiple choice question, the correct statement regarding the conversion is (c) Both CNF and DNF can be converted to each other interchangeably. This means any boolean expression can be converted into either CNF or DNF without loss of correctness.

Regarding the second part of the question with the algebraic expressions involving factorization:

1. (a) If A × F = B × F, we cannot necessarily conclude A = B unless F is not zero. Factorization allows us to cancel out the common factor (F) if it is nonzero.
2. (b) If A / F = B / F and F is not zero, then A = B can be true because both sides are divided by the same nonzero number.
3. (c) If F × A = B × F, this is the same as part (a) and we again cannot necessarily conclude A = B unless F is not zero.