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 function Y = AB + A(A +C) + B(A + C), we can use the rules of Boolean Algebra to combine terms.
Expanding the expression inside the parentheses by applying the Distributive Property:
Y = AB + AA + AC + BA + BC
Simplifying the expression by replacing any term that has a variable ANDed with its complement with 0:
Y = AB + 0 + AC + BA + BC
Simplifying further by replacing any term that has a variable ANDed with itself with the variable:
Y = AB + AC + BA + BC
Combining terms that are equivalent to a single variable:
Y = A + AC + B(A + C)
Using the Distributive Property again:
Y = A + AC + AB + BC
Simplifying the expression by combining like terms:
Y = A + AC + AB + BC
The final simplified expression is: Y = A + C(B + B).
Correct Answer: Y = A + C