This implies that quantity demanded increases when price decreases. Is this always true?

While it is generally true that quantity demanded increases as price decreases, this relationship is not absolute. Factors such as consumer preferences, income levels, and the availability of substitutes can influence demand. Additionally, for certain goods known as Giffen or Veblen goods, the relationship may not hold, as demand may rise even with higher prices. Thus, the law of demand applies in many cases, but exceptions exist.