Topic: Digital Circuits
The Boolean expression for the shaded area in the Venn diagram is (Venn diagram with sets X, Y, Z where the intersection of X and Y is shaded, as well as the region of Z excluding X and Y)
- A. X_bar + Y_bar + Z
- B. X*Y_bar*Z_bar + X_bar*Y*Z
- C. X + Y + Z
- D. X_bar*Y_bar*Z + X*Y
Answer: D. X_bar*Y_bar*Z + X*Y
Explanation: Based on the provided Venn diagram, the shaded regions represent the intersection of sets X and Y (which is X*Y) and the region of Z that does not intersect with either X or Y (which is X_bar*Y_bar*Z). The logical OR of these two disjoint regions gives the expression X_bar*Y_bar*Z + X*Y.