Question

Using rules of Boolean Algebra to Simplifiy the following Boolean function, chooes the correct answer ?
begin mathsize 16px style Y equals A B plus A left parenthesis A plus C right parenthesis plus B left parenthesis A plus C right parenthesis end style

Answer 1

To simplify the given Boolean expression using the rules of Boolean Algebra, we can apply the following steps:


Distribute the OR operator "+" over the terms inside the parentheses:
Y = AB + AA + AC + BA + BC


Replace any term that has a variable ANDed with its complement with 0:
Y = AB + 0 + AC + BA + BC


Replace any term that has a variable ANDed with itself with the variable:
Y = AB + AC + BA + BC


Since AB + BA is equivalent to A, we can simplify this expression further:
Y = A + AC + BC


So, the simplified Boolean expression is Y = A + AC + BC.
Therefore, the correct answer is: Y = A + AC + BC.