Aspire Faculty ID #18542 · Topic: UGC NET Computer Science Dec 2022 Shift I (Paper II) · Just now
UGC NET Computer Science Dec 2022 Shift I (Paper II)

Consider the Boolean expression given by


$F=(X+Y+Z)(X'+Y)(Y'+Z)$


Which of the following Boolean expressions is/are equivalent to $F'$?


A. $(X'+Y'+Z')(X+Y')(Y+Z')$


B. $(XY'+Z')$


C. $(X+Z')(Y'+Z')$


D. $(XY'+YZ'+X'Y'Z')$

Solution

$F=(X+Y+Z)(X'+Y)(Y'+Z)$

Taking complement,

$F'=(X+Y+Z)' + (X'+Y)' + (Y'+Z)'$

Using De Morgan's law,

$F'=X'Y'Z' + XY' + YZ'$

So,

$F'=XY'+YZ'+X'Y'Z'$

This matches statement D.

Now simplify:

$F'=XY'+YZ'+X'Y'Z'$

$=XY'+Z'(Y+X'Y')$

$=XY'+Z'(Y+X')$

$=XY'+YZ'+X'Z'$

This is also equivalent to:

$XY'+Z'$

So, statement B is correct.

Also,

$(X+Z')(Y'+Z')$

$=XY'+XZ'+Y'Z'+Z'$

$=XY'+Z'$

So, statement C is also correct.

Statement A is not equivalent.

Therefore, correct statements are B, C and D.

So, correct option is:

$\boxed{(b)\ \text{B, C and D Only}}$

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