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Consider the circuit shown below. The output of a 2:1 Mux is given by the function $(ac' + bc)$.

Which of the following is true?

1. $f=X1'+X2$
2. $f=X1'X2+X1X2'$
3. $f=X1X2+X1'X2'$
4. $f=X1+X2'$
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g = (a and x1′) or (b and x1)
g = (1 and x1’) or (0 and x1)
g = x1’

f = ac’ + bc
f = (a and x2′) or (b and x2)
f = (g and x2′) or (x1 and x2)
f = x1’x2’ + x1x2

Ref: Geeksforgeeks.org

g = x1'
So, f = ac' + bc

= x1'x2' + x1x2

So, (C).
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What is the significance of ac'+bc here?

We don't need it to get the answer. So why it is mentioned in the question?
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here , f = ac'+bc where for first mux c = x1 and for second mux c = x2.

Now substitute for g = ac' + bc => a x1' + b x , now for f , f= ac'+bc => g x2' + x1 x2 => x1' x2' + x1 x2.
+1 vote
Given output of the mux is $a{c}' + bc$

For the first mux, $g$ is the output and $a=0,b=1,c = x_{1}$

Hence,

$g=1.{x_{1}}'+0.x_{1} = {x_{1}}'$  $........(1)$

For the second mux,

$a=g={x_{1}}' [from (1)],b=x_{1},c=x_{2}$

$f={x_{1}}'.{x_{2}}'+x_{1}.x_{2}$

Hence, option (c).

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