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The Boolean expression XY + (X' + Y') Z is equivalent to
- a)XYZ' + X'Y'Z
- b)X'Y'Z' + XYZ
- c)(X + Z) (Y + Z)
- d)(X' + Z) (Y'Z)
Correct answer is option 'C'. Can you explain this answer?
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The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ...
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The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ...
Explanation:
The given Boolean expression is XY (X Y) Z.
We can simplify this expression using the distributive law of Boolean algebra, which states that:
X (Y Z) = XY XZ
Using this law, we can rewrite the expression as:
XY (X Y) Z
= XY XZ YZ (Applying distributive law)
= X (Y Z) YZ (Grouping like terms)
= (X Z) (Y Z) (Applying distributive law)
Therefore, the given Boolean expression XY (X Y) Z is equivalent to (X Z) (Y Z).
Hence, the correct answer is option C, (X Z) (Y Z).
Note: The distributive law is a very useful tool in simplifying Boolean expressions. It helps to reduce the number of terms and makes the expression easier to work with.
The given Boolean expression is XY (X Y) Z.
We can simplify this expression using the distributive law of Boolean algebra, which states that:
X (Y Z) = XY XZ
Using this law, we can rewrite the expression as:
XY (X Y) Z
= XY XZ YZ (Applying distributive law)
= X (Y Z) YZ (Grouping like terms)
= (X Z) (Y Z) (Applying distributive law)
Therefore, the given Boolean expression XY (X Y) Z is equivalent to (X Z) (Y Z).
Hence, the correct answer is option C, (X Z) (Y Z).
Note: The distributive law is a very useful tool in simplifying Boolean expressions. It helps to reduce the number of terms and makes the expression easier to work with.
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The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer?
Question Description
The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer?.
The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Boolean expression XY + (X + Y) Z is equivalent toa)XYZ + XYZb)XYZ + XYZc)(X + Z) (Y + Z)d)(X + Z) (YZ)Correct answer is option 'C'. Can you explain this answer?.
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