Page 47 - Computer science 868 Class 12
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6.  The Boolean equation which holds true for the Involution law is                          [ISC 2021]
                       a.  A'+1 = 1                                    b.  ((A+B)')' = A+B
                       c.  (A+B)' = A'.B'                              d.  A.(B+C) = A.B+A.C
                    7.  The representation of the Boolean function F(A, B) = π(1, 3) in the canonical form is    [ISC 2021]
                       a.  (A'+B).(A+B)                                b.  Σ(0,2)
                       c.  A'.B+A.B                                    d.  (A+B').(A'+B')
                    8.  If, P=1, Q=1, R=0 and S=1, then the minterm will be                                      [ISC 2021]
                       a.  P+Q+R'+S                                    b.  P'.Q'.R.S'
                       c.  P.Q.R'.S                                    d.  P'+Q'+R+S'
                    9.  The dual of the Boolean expression (X+Y)'+X'.Y'+1 = 1 is                                 [ISC 2021]
                       a.  (X.Y)'.(X'+Y').0 = 0                        b.  (X+Y)'.X'.Y'+1 = 1
                       c.  (X.Y).(X+Y).0 = 0                           d.  (X.Y)'.(X'+Y').1 = 1
                    10.  The complement of the Boolean expression (P.Q)'+R' is                      [ISC Specimen Paper 2022]
                       a.  (P+Q).R                                     b.  P.Q.R
                       c.  (P'+Q').R'                                  d.  (P'+Q').R
                    11.  The law which states a+b.c = (a+b).(a+c) is                                [ISC Specimen Paper 2022]
                       a.  Associative law                             b.  Distributive law
                       c.  Involution law                              d.  Commutative law
                   Answers
                     1.  d         2.   d           3.  c         4.  a           5.  b          6.  b       7.  c
                     8.  c         9.  a           10.  d        11.  b

                 B.  Fill in the blanks:
                    1.  The boolean expression A.A'=0 represents ………………… law.
                    2.  (A+B+C)' is equal to ………………… according to De Morgan’s law.
                    3.  The dual of A+1 = 1 is ………………… .
                    4.  A truth table of 4 variables has ………………… input combinations.
                    5.  If, X=1, Y=0 and Z=1, then its minterm is ………………… .
                    6.  A → B is equivalent to ………………… .
                    7.  (A → B).(B → A) is an expression for ………………… .
                    8.  Compound propositions are joined by the ………………… .
                    9.  A.0 = 0 is an example of ………………… .
                   10.  Canonical SOP form of F(A, B, C) = Σ(4, 5) is ………………… .

                   Answers
                     1.  Complement    2.  A'.B'.C'    3.  A.0=0       4.  16          5.  X.Y'.Z     6.  A'+B
                     7.  Biconditional   8.  connectives     9.  Contradiction     10.  A.B'.C' + A.B'.C


                 C.  Answer the following questions:
                    1.  Draw the truth table of
                       (i)  conditional
                      (ii)  biconditional
                   Ans.    a         b       a → b     a ↔ b
                           0         0         1         1
                           0         1         1         0
                           1         0         0         0
                           1         1         1         1





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