One easy way to construct a logic gate implementation from a truth table is to recognize that the output is the OR of every row that has a 1 as the result. Each row is the AND of every column that has a 1 in it. Given the following Boolean expression:

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

determine the truth table; then implement the result using NAND gates. You may use three input NAND gates if necessary.