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in given combinational logic $X=?$

  1. $X = AB'C' +A'BC'+ A'B'C+ ABC$
  2. $X = A'BC +A'BC'+ AB'C+ A'B'C'$
  3. $X = AB + BC + AC$
  4. $X= A'B'+B'C'+A'C'$
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The output expression of 1st multiplexer is:

$ Y=\bar A\bar BI_0+\bar A BI_1+ A\bar BI_2+ A BI_3$

$Y=\bar A\bar B.0+\bar A B.1+ A\bar B.1+ A B.0$

$Y=\bar A B+ A\bar B= A\oplus B$

The output expression of 2nd multiplexer is:

$X=\bar Y\bar CI_0+\bar Y CI_1+ Y\bar CI_2+ YCI_3$

$X=\bar Y\bar C.0+\bar Y C.1+ Y\bar C.1+ YC.0$

$X=\bar Y C+ Y\bar C$

$X=(\overline{A\oplus B}) C+ (A\oplus B)\bar C$

$X=(\bar A\bar B+AB)C+(\bar AB+A\bar B) \bar C$

$X=\bar A\bar BC+ABC+\bar AB\bar C+A\bar B\bar C$

Option $(B)$ is correct.

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