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If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y + yz + z + xz is equivalent to
- a)xy + yz + zx
- b)x + y + z
- c)xyz
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y ...
Boolean Algebraic Simplification
Boolean algebra is a branch of algebra in which variables can take only two values, either true or false. Boolean algebra simplifies the logical expressions and reduces them to the simplest form. Boolean algebra rules are applied to simplify the Boolean expressions.
Steps to Simplify Boolean Expression
The following are the steps to simplify the given Boolean expression:
1. Identify the terms with common variables.
2. Use Boolean algebra rules to simplify the expression.
3. Combine the terms to obtain the simplified expression.
Simplifying F(x,y,z) = x xy y yz z xz
The given Boolean expression is:
F(x,y,z) = x xy y yz z xz
Step 1: Identify the terms with common variables.
The term xy and xz have x as a common variable.
Step 2: Use Boolean algebra rules to simplify the expression.
Using the distributive property, we can write:
F(x,y,z) = x(y + z) + yz
Using the distributive property again, we get:
F(x,y,z) = xy + xz + yz
Step 3: Combine the terms to obtain the simplified expression.
The simplified Boolean expression is:
F(x,y,z) = xy + xz + yz
Therefore, the equivalent expression of F(x,y,z) = x xy y yz z xz is xy + xz + yz, which is option B.
Boolean algebra is a branch of algebra in which variables can take only two values, either true or false. Boolean algebra simplifies the logical expressions and reduces them to the simplest form. Boolean algebra rules are applied to simplify the Boolean expressions.
Steps to Simplify Boolean Expression
The following are the steps to simplify the given Boolean expression:
1. Identify the terms with common variables.
2. Use Boolean algebra rules to simplify the expression.
3. Combine the terms to obtain the simplified expression.
Simplifying F(x,y,z) = x xy y yz z xz
The given Boolean expression is:
F(x,y,z) = x xy y yz z xz
Step 1: Identify the terms with common variables.
The term xy and xz have x as a common variable.
Step 2: Use Boolean algebra rules to simplify the expression.
Using the distributive property, we can write:
F(x,y,z) = x(y + z) + yz
Using the distributive property again, we get:
F(x,y,z) = xy + xz + yz
Step 3: Combine the terms to obtain the simplified expression.
The simplified Boolean expression is:
F(x,y,z) = xy + xz + yz
Therefore, the equivalent expression of F(x,y,z) = x xy y yz z xz is xy + xz + yz, which is option B.
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Community Answer
If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y ...
=x(1+y)+y(1+z)+z(1+x)
=x•1+y•1+z•1. as we know 1+x=1
=x+y+z
=x•1+y•1+z•1. as we know 1+x=1
=x+y+z
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If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y + yz + z + xz is equivalent toa)xy + yz + zxb)x + y + zc)xyzd)1Correct answer is option 'B'. Can you explain this answer?
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If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y + yz + z + xz is equivalent toa)xy + yz + zxb)x + y + zc)xyzd)1Correct answer is option 'B'. 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 If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y + yz + z + xz is equivalent toa)xy + yz + zxb)x + y + zc)xyzd)1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y and z are three Boolean variables, then F(x,y,z) = x + xy + y + yz + z + xz is equivalent toa)xy + yz + zxb)x + y + zc)xyzd)1Correct answer is option 'B'. Can you explain this answer?.
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