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8. Draw the logical diagram and truth table for a 2-input XNOR gate. [ISC 2017]
Ans. The truth table and logical circuit diagram of a 2 variable XNOR gate is given below:
A B A ⊙ B
0 0 1
0 1 0
1 0 0
1 1 1
A A.B
B
A'.B' + A.B
A' A'.B'
B'
9. Show that X ∨ ∼(Y ∧ X) is a tautology. [ISC 2016]
Ans. X Y ∼(Y ∧ X) X ∨ ∼(Y ∧ X)
0 0 1 1
0 1 1 1
1 0 1 1
1 1 0 1
The final column has a value 1. Hence, it is a tautology.
10. State whether the following expression is a Tautology, Contradiction or a Contingency, with the help of a truth table:
(X → Z) ∨ ∼[(X → Y) ∧ (Y → Z)]. [ISC 2016]
Ans. X Y Z (X → Z) (X → Y) (Y → Z) (X → Y) ∧ (Y → Z) (X → Z) ∨ ∼[(X → Y) ∧ (Y → Z)]
0 0 0 1 1 1 1 1
0 0 1 1 1 1 1 1
0 1 0 1 1 0 0 1
0 1 1 1 1 1 1 1
1 0 0 0 0 1 0 1
1 0 1 1 1 1 1 1
1 1 0 0 0 0 0 1
1 1 1 1 1 1 1 1
Since the final column has 1 as its truth value in all combinations, it is a tautology.
9696 Touchpad Computer Science-XI

