3. What is the relationship between entropy and information gain? High entropy and high information gain is desired. When information gain decreases, entropy decreases. High entropy and low information gain is desired. When information gain increases, entropy decreases.

The correct answer is: When information gain increases, entropy decreases.<br /><br />Entropy is a measure of the uncertainty or randomness in a system, while information gain is a measure of the reduction in uncertainty or the amount of information obtained from a decision. In general, when information gain increases, it means that the decision tree is becoming more accurate in separating the data into different classes, which leads to a decrease in entropy. Conversely, when information gain decreases, it means that the decision tree is becoming less accurate in separating the data, which leads to an increase in entropy. Therefore, the relationship between entropy and information gain is that when information gain increases, entropy decreases.