Page 29 - Computer science 868 Class 12
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0      1      1      0       0       1        0       1       1       1       1
                             1      0      0      0       0       0        0       1       1       0       1
                             1      0      1      0       0       0        0       1       1       1       1
                             1      1      0      1       0       0        0       1       1       1       1
                             1      1      1      1       1       1        1       1       1       1       1

                 7.  Distributive Law
                   This law states that
                   •   the product of two variables, when added to a third variable, produces the same result as separately adding each
                     variable with the third variable and multiplying their sums.
                   •   the sum of two variables, when multiplied to a third variable, produces the same result as separately multiplying
                     each variable with the third variable and adding their products.
                   The above laws can be expressed algebraically as follows:
                   A.(B+C) = A.B + A.C
                   A + B.C = (A+B).(A+C)
                   The proof of the above expressions using the truth table is as follows:

                                   A        B        C       A.(B+C)     A.B+A.C      A+B.C     (A+B).(A+C)
                                   0        0        0         0            0           0           0
                                   0        0        1         0            0           0           0
                                   0        1        0         0            0           0           0
                                   0        1        1         0            0           1           1
                                   1        0        0         0            0           1           1
                                   1        0        1         1            1           1           1
                                   1        1        0         1            1           1           1
                                   1        1        1         1            1           1           1
                 8.  Absorption Law
                   This law is a modified Distributive law where a Boolean variable is ‘absorbed’ or eliminated in a Boolean expression,
                   thus simplifying it.

                                      A          B          A+B       A.(A+B)       A.B        A+A.B
                                      0          0           0           0           0           0
                                      0          1           1           0           0           0
                                      1          0           1           1           0           1
                                      1          1           1           1           1           1

                   The law when expressed algebraically is given as:
                   A.(A+B) = A
                   A + A.B = A
                   The proof using the truth table is given here.
                 9.  De Morgan’s Law
                   This law states that
                   •  the complement of the sum of two Boolean variables is equal to the product of its individual complemented terms.
                   •   the complement of the product of two Boolean variables is equal to the sum of its individual complemented
                     terms.



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