Aspire Faculty ID #16260 · Topic: NIMCET 2011 · Just now
NIMCET 2011

Which of the following Boolean expression represents the shaded portion of the Venn diagram? Note: Here "." represents an AND operation and "+" denotes an OR operation.

Solution

The shaded region is the part common to all three sets X, Y, Z (the triple overlap).

That means the region represents:

X ∙ Y ∙ Z

Now check options:

Option (2):
Z.(X + Y) = ZX + ZY
This includes regions where Z overlaps with X OR Z overlaps with Y — this is larger than triple intersection → NOT correct.

Option (3):
(Z.X′) + Y
This includes all of Y plus some part of Z, totally incorrect.

Option (1):
Z′ + (X.Y)
This includes all outside Z plus XY, wrong.

Option (4):
Z′.(X + Y)
This is the region outside Z but inside X or Y, wrong.
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