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

option 1 is misprint, pz correct it

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Option a is misprint check it

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option A) still have mistake?

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

can you pls tell me, how you are applying distributive property to get next expression

wx + xy + wy

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Option A

Should be :

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

= wx+wx+wy+x+xy

= wx+wy+x

= x+wy

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@Arjun sir please correct the option A in above question.

It must be wx + w(x+y) + x(x+y) = x + wy .
If it is wx+w(x+y)+x(xy)=x+wy then on placing w=0,x=1,y=0 we wont get L.H.S and R.H.S same.

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Fast method: Put $w=1, x=0,y=1$, we will see LHS and RHS don’t match for Option C.

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

option c is incorrect as we will get ~xy+~xy~w on simplification