Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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:
$\boxed{(b)\ \text{B, C and D Only}}$
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
