IB JIO Grade-2 Tech 2023 part-2: 16

Question

Q.16 Simplify the Boolean expression.
\[
Y=A B+A(B+C)+B(B+C)
\]
Ans
1. $Y=B+A C$
2. $Y=A+B C$
3. $Y=C+A B$
4. $Y=A C$
Question ID : 630680278458
Option 1 ID : 6306801082190
Option 2 ID : 6306801082189
Option 3 ID : 6306801082191
Option 4 ID : 6306801082192
Status : Answered
Chosen Option : 2

Answer 1

$Y=AB+A(B+C)+B(B+C)$

$Y=AB+AB+AC+B+BC$

taking $B$ as common we get:

$Y=B(A+A+1+C)+AC$

$\because A+1=1$

$\therefore Y=B+AC$

Option $(1)$ is correct.