GATE CSE 2017 | Set 2 | Question: 27

Question

If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT?

• A. $wx+w(x+y)+x(x +y) = x+wy$
• B. $\overline{w \bar{x}(y+\bar{z})} + \bar{w}x = \bar{w} + x + \bar{y}z$
• C. $(w \bar{x}(y+x\bar{z}) + \bar{w} \bar{x}) y = x \bar{y}$
• D. $(w+y)(wxy+wyz) = wxy+wyz$

Comments

The most efficient method is to apply the By-Case method....

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Detailed Video Explanation with multiple ways to solve: https://youtu.be/3Wj-BXY41MU?t=4876

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Don't Solve all the option
Always put the values this type of question
Like put W=1 in all the option bot side Automatic A,B,D is match in RHS and LHS
Hence Option C is Correct

Answer 1

Let us try to simplify (minimize) the expression given in each option

Option - A: $wx+w(x+y)+x(x+y)=x+wy$

$wx + wx + wy + x$
$wx + wy + x$    
$x (1+w) + wy$                  
$x  + wy$

Option - B:  $\overline{w \bar{x}(y+\bar{z})} + \bar{w}x = \bar{w} + x + \bar{y}z$

$\overline{w\bar{x}} + \overline{(y+\bar{z})} + \bar{w}x$
$\bar{w} + x + \bar{y}z + \bar{w}x$
$\bar{w} + \bar{w}x + x + \bar{y}z$
$\bar{w} + x + \bar{y}z$

Option - D: $(w+y)(wxy+wyz)=wxy+wyz$

$wxy + wyz + wxy + wyz$
$wxy + wyz$

Option A, B, D are matching fine.

Hence, Option - C is the answer

Comments

@Abhrajyoti00 but choosing these values sometimes will land up wrong result like if we put $x=1,y=1,w=0$ so first will give same for LHS and RHS but its incorrect so instead of this We can use by case method where we can choose one variable value as either 1 or 0 and check for both the cases

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Common Identitis to remember 

 

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can i do like put anything or any specific trick

 

Answer 2

Option C-(wx'(y+xz')+w'.x')y= (wx'y+wx'xz'+w'x')y=
xx'=0 ..so
Wx'y+w'x'y=x'y(w+w')=x'y

Comments

HOW IS A CORRECT??

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1st option given here is not the one they asked..the 1 st option is:

wx+w(x+y)+x(x+y)=x+wy

wx+wx+wy+x+xy

wx+wy+x(1+y)

wx+wy+x

x(w+1)+wy

x+wy

Answer 3

LHS = (wx'(y + xz') + w'x')y = x'y

RHS =xy'

Option C-   Put y=0 and see LHS !=RHS

Comments

x(w+1) =x.1=x ans is C

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BOTH A AND C ARE INCORRECT.

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No only C is Not correct

Answer 4

Just observe option C: on the LHS, there is no y' term, but on the RHS, there is y'. Unless we fully complement the LHS, we won't get y' on the RHS. However, we are not complementing the LHS, so option C is the only false one.

Answer 5

Here is the Explanation and correct answer is option -C ✅