Final answer:
Well-defined sets have precise membership criteria, and among the options, the colors of the rainbow, points on a straight line, and the consonants of the English alphabet are well-defined. Honesty in a family is subjective and cannot form a well-defined set.
Step-by-step explanation:
In mathematics, a well-defined set has clear and precise membership criteria that determines whether an object is a member of the set or not. Let's examine the options provided:
- All the colors in the rainbow is a well-defined set because there is a clear and common understanding of what the colors in the rainbow are: red, orange, yellow, green, blue, indigo, and violet.
- All the points that lie on a straight line is also a well-defined set as in geometry, points on a straight line can be clearly identified and agreed upon using mathematical properties or coordinates.
- All the honest members in the family is not a well-defined set because honesty is a subjective quality and cannot be measured or defined clearly for the purposes of set membership.
- All the consonants of the English alphabet is a well-defined set because the consonants are specifically identified letters that exclude the vowels (A, E, I, O, U), in the English language, leaving a specific list of consonants that can be consistently identified.
Options A, B, and D represent well-defined sets: the colors of the rainbow, points on a straight line, and consonants of the English alphabet. Option C is not well-defined due to the subjective nature of honesty.