The Boolean equation X=[(A+{B})(B+C)] B can be simplified to

Correct Answer is : X=ABX = ABX=AB

Correct Answer is : X=ABX = ABX=AB

Test Index

RRB Technician Grade 1 Model Paper 1

Question : 88 of 100

Marks: +1, -0

X=[(A+\bar{B})(B+C)] B

can be simplified to

Solution:

Concept:

Use Boolean algebra laws to expand and simplify the given expression.

Explanation:

Start with

X = [(A + \overline{B})(B + C)]B

First expand

(A + \overline{B})(B + C)

using the distributive law:

(A + \overline{B})(B + C) = AB + AC + \overline{B}B + \overline{B}C

Since

\overline{B}B = 0

, this becomes

AB + AC + \overline{B}C

Now multiply the whole term by

B

X = (AB + AC + \overline{B}C)B

This gives

X = ABB + ABC + \overline{B}CB

Simplify each term:

ABB = AB

ABC

stays as

ABC

, and

\overline{B}CB = 0

because

\overline{B}B = 0

X = AB + ABC = AB(1 + C)

Using the null law,

1 + C = 1

Therefore,

X = AB

Answer:

X = AB

, so the correct option is C.

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