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The Boolean expression AB + AC̅ + BC simplifies to
- a)BC + AC̅
- b)AB + AC̅ + B
- c)AB + AC̅
- d)AB + BC
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The Boolean expression AB + AC + BC simplifies toa)BC + ACb)AB + AC + ...
Explanation:
The given Boolean expression is AB • AC • BC.
To simplify this expression, we can use Boolean algebra rules and laws.
Distributive Law:
The Distributive Law states that AB + AC = A(B + C). Similarly, AB • AC = A • (B • C).
Using the Distributive Law:
AB • AC • BC = A • (B • C) • BC
Associative Law:
The Associative Law states that A • (B • C) = (A • B) • C.
Using the Associative Law:
A • (B • C) • BC = (A • B) • C • BC
Identity Law:
The Identity Law states that A • 1 = A and A + 0 = A.
Using the Identity Law:
(A • B) • C • BC = (A • B) • C • BC • 1
Commutative Law:
The Commutative Law states that AB = BA and A + B = B + A.
Using the Commutative Law:
(A • B) • C • BC • 1 = (A • B) • BC • C • 1
Identity Law:
Again, using the Identity Law, BC • C • 1 = BC.
Final Simplification:
Therefore, the simplified Boolean expression is (A • B) • BC.
Explanation of the Correct Answer:
The correct answer is option 'A' which is BC • AC. This is the correct simplification of the given Boolean expression AB • AC • BC.
The given Boolean expression is AB • AC • BC.
To simplify this expression, we can use Boolean algebra rules and laws.
Distributive Law:
The Distributive Law states that AB + AC = A(B + C). Similarly, AB • AC = A • (B • C).
Using the Distributive Law:
AB • AC • BC = A • (B • C) • BC
Associative Law:
The Associative Law states that A • (B • C) = (A • B) • C.
Using the Associative Law:
A • (B • C) • BC = (A • B) • C • BC
Identity Law:
The Identity Law states that A • 1 = A and A + 0 = A.
Using the Identity Law:
(A • B) • C • BC = (A • B) • C • BC • 1
Commutative Law:
The Commutative Law states that AB = BA and A + B = B + A.
Using the Commutative Law:
(A • B) • C • BC • 1 = (A • B) • BC • C • 1
Identity Law:
Again, using the Identity Law, BC • C • 1 = BC.
Final Simplification:
Therefore, the simplified Boolean expression is (A • B) • BC.
Explanation of the Correct Answer:
The correct answer is option 'A' which is BC • AC. This is the correct simplification of the given Boolean expression AB • AC • BC.
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Community Answer
The Boolean expression AB + AC + BC simplifies toa)BC + ACb)AB + AC + ...
Concept:
3 variable K-maps:
3 variable K-maps:
- For a 3-variable Boolean function, there is a possibility of 8 output minterms.
- The general representation of all the minterms using 3-variables is shown below.
Calculation:
Given Boolean expression is,
F = AB + AC̅ + BC
= A B C̅ + A B C + A B̅ C̅ + A B C̅ + A B C + A̅ B C
F = BC + AC̅
Given Boolean expression is,
F = AB + AC̅ + BC
= A B C̅ + A B C + A B̅ C̅ + A B C̅ + A B C + A̅ B C
F = BC + AC̅
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The Boolean expression AB + AC + BC simplifies toa)BC + ACb)AB + AC + Bc)AB + ACd)AB + BCCorrect answer is option 'A'. Can you explain this answer?
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