# GATE2005-15

2.9k views

Consider the following circuit.

Which one of the following is TRUE?

1. $f$ is independent of $x$

2. $f$ is independent of $y$

3. $f$ is independent of $z$

4. None of $x, y, z$ is redundant

edited

The expression will be

$f = [ ( x.y' )'.(y.z) ]'=[ (x'+y).(y.z) ]' =[ x'.y.z+y.z ]'=[ (x'+1).(y.z) ]'=[ 1.(y.z) ]'=[ y.z ]'=y'+z'$

The final expression only contains $y$ and $z$,

Therefore, answer will be (a) f is Independent of $x$

edited
0
f= (x'+y)'+(yz)'    //here i have applied "bubble OR Gate"

=(xy')+(y'+z')

=y'(x+1)+z'

=y'+z'               //A+A'=1

Simplify the given circuit, as dotted input OR gate is equal to NAND gate:

(A) is the correct option!

edited
ans a)
0
can you give solution??

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