Question

Minimise the following:A+{A.(B.C)}

Answer 1

Given:

     A+{A.(B.C)}

To find:

    Minimize the above expression

solution:

                      A+{A.(B.C)}

                     = A+{ABC}

                     = A+ABC

                     =A.{1+BC}

we know that as per distributive law in boolean algebra,

                      (x + yz) = (x + y) (x + z)

                      here, x = 1, y = B, z = C

        so, we get

                    =A.{(1+B).(1+C)}  

now as per law of addition in boolean algebra,

                    (1+B) = 1   and (1+C) = 1

so, we get                                              

                 =A.{(1).(1)} =A.{1}

                 =A

Answer:

      So the answer is A+{A.(B.C)} = A

Answer 2

Given :

A+{A.(B.C)}

To find :

Equivalent value of equation A+{A.(B.C)}

Solution :

Truth table method

A+{A.(B.C)}

ABC  B.C   A.(B.C)   A+{A.(B.C)}

000    0         0                0

001     0         0                0

010     0         0                0

011      1          0                0

100    0          0                1

101     0          0                1

110     0          0                1

111      1           1                 1

We will compare the truth values.

Since the truth value of A and A+{A.(B.C)} are same.

Therefore, A+{A.(B.C)} = A

A+{A.(B.C)} = A