GATE Exam > GATE Questions > If w, x, y, z are boolean variables, then whi...
Start Learning for Free
If w, x, y, z are boolean variables, then which of the following in INCORRECT?
- a)wx + w(x+y) + x(x+y) = x + wy
- b)(wx'(y + z'))' + w'x = w' + x + y'z
- c)(wx'(y + xz') + w'x')y = xy'
- d)(w + y)(wxy + wyz) = wxy + wyz
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If w, x, y, z are boolean variables, then which of the following in IN...
Most Upvoted Answer
If w, x, y, z are boolean variables, then which of the following in IN...
Explanation:
To determine which of the given options is incorrect, we need to evaluate each option one by one and check if it violates any rules or properties of boolean algebra. Let's analyze each option:
Option A: wx w(x y) x(x y) = x wy
- Distributive law: w(x y) = wx wy
- Associative law: (wx wy) x(x y) = wx wy x(x y) = wx wy
- Simplification: wx wy = wx wy
- Therefore, option A is correct.
Option B: (wx(y z)) wx = w x yz
- Distributive law: wx(y z) = wxy wxz
- Associative law: (wxy wxz) wx = wxy wxz wx
- Simplification: wxy wxz wx = wxy wxz wx
- Therefore, option B is correct.
Option C: (wx(y xz)) wx)y = xy
- Distributive law: wx(y xz) = wxy wxz
- Associative law: (wxy wxz) wx)y = wxy wxz wx)y
- Simplification: wxy wxz wx)y = wxy wxz wx)y
- Therefore, option C is incorrect.
Option D: (w y)(wxy wyz) = wxy wyz
- Distributive law: (w y)(wxy wyz) = w(wxy wyz) y(wxy wyz)
- Simplification: w(wxy wyz) y(wxy wyz) = w^2xy w^2yz wxy wyz
- Simplification: w^2xy w^2yz wxy wyz = wxy wyz
- Therefore, option D is correct.
Therefore, the correct answer is option C.
To determine which of the given options is incorrect, we need to evaluate each option one by one and check if it violates any rules or properties of boolean algebra. Let's analyze each option:
Option A: wx w(x y) x(x y) = x wy
- Distributive law: w(x y) = wx wy
- Associative law: (wx wy) x(x y) = wx wy x(x y) = wx wy
- Simplification: wx wy = wx wy
- Therefore, option A is correct.
Option B: (wx(y z)) wx = w x yz
- Distributive law: wx(y z) = wxy wxz
- Associative law: (wxy wxz) wx = wxy wxz wx
- Simplification: wxy wxz wx = wxy wxz wx
- Therefore, option B is correct.
Option C: (wx(y xz)) wx)y = xy
- Distributive law: wx(y xz) = wxy wxz
- Associative law: (wxy wxz) wx)y = wxy wxz wx)y
- Simplification: wxy wxz wx)y = wxy wxz wx)y
- Therefore, option C is incorrect.
Option D: (w y)(wxy wyz) = wxy wyz
- Distributive law: (w y)(wxy wyz) = w(wxy wyz) y(wxy wyz)
- Simplification: w(wxy wyz) y(wxy wyz) = w^2xy w^2yz wxy wyz
- Simplification: w^2xy w^2yz wxy wyz = wxy wyz
- Therefore, option D is correct.
Therefore, the correct answer is option C.
|
Explore Courses for GATE exam
|
|
If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer?
Question Description
If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect 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 If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect 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 If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer?.
If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect 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 If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect 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 If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If w, x, y, z are boolean variables, then which of the following in INCORRECT?a)wx + w(x+y) + x(x+y) = x + wyb)(wx'(y + z'))' + w'x = w' + x + y'zc)(wx'(y + xz') + w'x')y = xy'd)(w + y)(wxy + wyz) = wxy + wyzCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup