Math Problem Statement
Answer the following question Which Boolean expression is equivalent to ¬ ( 𝐴 ∧ 𝐵 ) ¬(A∧B)?
Select your answer: Select your answer OPTION ALTERNATIVE A'
B'
A′∧B′
A′∨B′
None of the above
Solution
To determine which Boolean expression is equivalent to ¬(A ∧ B), we can use De Morgan's laws. De Morgan's laws state:
- ¬(A ∧ B) = ¬A ∨ ¬B
- ¬(A ∨ B) = ¬A ∧ ¬B
Applying the first law to ¬(A ∧ B):
¬(A ∧ B) = ¬A ∨ ¬B
Thus, the Boolean expression equivalent to ¬(A ∧ B) is A′ ∨ B′.
So the correct answer is: A′ ∨ B′
Would you like any further details or have any questions?
Here are some additional questions you might want to ask:
- How do De Morgan's laws work?
- Can you provide an example using De Morgan's laws?
- What are some applications of De Morgan's laws in digital circuits?
- How can I simplify a Boolean expression using Boolean algebra rules?
- What is the difference between a conjunction and a disjunction in Boolean algebra?
Tip: When working with Boolean expressions, always remember to apply De Morgan's laws to simplify expressions involving negations.
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Math Problem Analysis
Mathematical Concepts
Boolean Algebra
De Morgan's Laws
Formulas
-
Theorems
De Morgan's Laws
Suitable Grade Level
High School