AP Computer Science A Standards: Boolean expressions can often be simplified or rewritten to be logically equivalent. De Morgan's Laws state that !(A && B) is equivalent to !A || !B, and !(A || B) is equivalent to !A && !B. Recognizing equivalent expressions is crucial for optimizing conditions and understanding the control flow of complex decision structures. Truth tables can be used to prove that two expressions yield the exact same result for all possible inputs.