GATE 2017 CS (CS2) – Question 37

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple choice

For Boolean variables w,x,y,z, which identity is INCORRECT?

$wx+w(x+y)+x(x+y)=x+wy$
$\overline{w\bar x(y+\bar z)}+\bar wx=\bar w+x+\bar yz$
$(w\bar x(y+x\bar z)+\bar w\bar x)y=x\bar y$
$(w+y)(wxy+wyz)=wxy+wyz$

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Correct answer: (C) $(w\bar x(y+x\bar z)+\bar w\bar x)y=x\bar y$

Explanation

In C the left side simplifies to $w\bar xy+\bar w\bar xy=\bar xy$, not $x\bar y$. Set x=0,y=1 to obtain left side 1 and right side 0. A follows by absorption, B by De Morgan and absorption, and D because each term already contains w or y. Thus C is the false identity.

GATE 2017 CS (CS2) – Question 37

Explanation

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