Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalseSingle choice
A
True
B
False

Question

Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalse

BlackTom AI · Accepted Answer

Consider the claim about entropy for a homogeneous set, and examine each option carefully.
Option 1: 'True' — This statement would mean that a dataset where all instances share the same label can have nonzero entropy. In information theory, a completely uniform (homogeneous) distribution over classes yields maximum predictability for the single observed label, and thus zero entropy. Therefore, asserting that the entropy is not always zero is incorrect because, by definition, H = - sum p(i) log p(i) equals 0 when one class has probability 1 and all others have probability 0.
Option 2: 'False' — This aligns with the standard entropy calculation. Since a homogeneous set has p = 1 for the single label, the entropy H = -1 * log(1) = 0. There is no randomness across labels to contribute to uncertainty, so the entropy is zero. Any claim that entropy could be nonzero in this case contradicts the fundamental formula for entropy of a categorical distribution.

Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalseSingle choice

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