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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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The Boolean expression AB + AC + BC simplifies toa)BC + ACb)AB + AC + ...
Given Boolean expression is,
F = AB + AC̅ + BC
F = BC + AC̅
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The Boolean expression AB + AC + BC simplifies toa)BC + ACb)AB + AC + ...
Solution:
The given Boolean expression is AB AC BC.
To simplify this expression, we need to use Boolean algebra laws and simplify each term individually.
Using the distributive law, we can write AB AC BC as:
A(B+C)B
= AB + ACB (distributive law)
= AB + BC (since ACB = 0)
Therefore, the simplified expression is BC AC.
So, option A is the correct answer.
HTML representation:
Solution:
Given Boolean expression is AB AC BC.
To simplify the expression, we use Boolean algebra laws and simplify each term individually.
Using the distributive law, we get:
AB AC BC = A(B+C)B
= AB + ACB (distributive law)
= AB + BC (since ACB = 0)
Therefore, the simplified expression is BC AC.
Hence, option A is the correct answer.
The given Boolean expression is AB AC BC.
To simplify this expression, we need to use Boolean algebra laws and simplify each term individually.
Using the distributive law, we can write AB AC BC as:
A(B+C)B
= AB + ACB (distributive law)
= AB + BC (since ACB = 0)
Therefore, the simplified expression is BC AC.
So, option A is the correct answer.
HTML representation:
Solution:
Given Boolean expression is AB AC BC.
To simplify the expression, we use Boolean algebra laws and simplify each term individually.
Using the distributive law, we get:
AB AC BC = A(B+C)B
= AB + ACB (distributive law)
= AB + BC (since ACB = 0)
Therefore, the simplified expression is BC AC.
Hence, option A is the correct answer.
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