Page 74 - computer science (868) class 11
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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.
























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