Q42.Marks: +2.0UGC NET Paper 2: Computer Science 18th June 2024 Shift 1 (Cancelled)
Match List - I with List - II.
LIST - I
Boolean Expression
LIST - II
Dual of Boolean Expression
A.
x·(y + 0)
I.
(x̅ + 0) (y̅ · z)
B.
x̅·1 + (y̅ + z)
II.
x + y·1
C.
x̅·(y̅ + 0)
III.
x̅ + y̅·1
D.
x·1 + (y + z̅)
IV.
(x + 0)·(y + z̅)
Choose the correct answer from the options given below:
1.A - III, B - IV, C - II, D - I
2.A - III, B - IV, C - I, D - II
3.A - II, B - I, C - III, D - IV✓ Correct
4.A - II, B - I, C - IV, D - III
Solution
The correct answer is A - II, B - I, C - III, D - IV
Key PointsTo find the dual of a Boolean expression, you replace AND operations (·) with OR operations (+), OR operations (+) with AND operations (·), 0 with 1, and 1 with 0. Let's do this for each expression:
Step-by-Step Calculation:
Boolean Expression: x·(y + 0)
Dual: x + y.1
Boolean Expression: x̅·1 + (y̅ + z)
Dual: (x̅ + 0) (y̅ · z)
Boolean Expression: x̅·(y̅ + 0)
Dual: x̅ + y̅·1
Boolean Expression: x·1 + (y + z̅)
Dual: (x + 0)·(y + z̅)
So, the correct answer is A - II, B - I, C - III, D - IV