Question 32 (ii) (Choice 2) - Sample Paper 2 by Teachoo - Teachoo Sample Paper

Simplify the following Boolean expression using Boolean algebra rules:

(A + B) . (A' + B') + A

Answer:

Answer by student

The simplified expression is A .

The steps are:

• (A + B) . (A’ + B’) + A

• AA’ + AB’ + BA’ + BB’ + A (Distributive law)

• 0 + AB’ + BA’ + 0 + A (Complement law)

• AB’ + BA’ + A (Identity law)

• A(B’ + A’) + A (Distributive law)

• A(0) + A (Complement law)

• 0 + A (Identity law)

• A

Detailed answer by teachoo

To simplify the expression, we need to use some Boolean algebra rules. Here are some of the rules we will use:

• Complement law : X + X’ = 1 and X.X’ = 0
• Identity law : X + 0 = X and X.1 = X
• Distributive law : X(Y + Z) = XY + XZ and X + YZ = (X + Y)(X + Z)

Let’s see how to apply these rules step by step:

• The given expression is (A + B) . (A’ + B’) + A .
• We can use the distributive law to expand the product of the first two terms as follows: AA’ + AB’ + BA’ + BB’ + A .
• We can use the complement law to simplify the terms AA’ and BB’ as follows: 0 + AB’ + BA’ + 0 + A .
• We can use the identity law to simplify the terms 0 as follows: AB’ + BA’ + A .
• We can use the distributive law again to factor out A from the first two terms as follows: A(B’ + A’) + A .
• We can use the complement law again to simplify the term (B’ + A’) as follows: A(0) + A .
• We can use the identity law again to simplify the term A(0) as follows: 0 + A .
• We can use the identity law one more time to simplify the term 0 as follows: A .

This is the final simplified expression. So, the correct answer is A.