Final answer:
Well-defined sets are those without ambiguity regarding membership. Colors of the rainbow, points on a line, consonants in the alphabet, prime numbers less than 100, and letters in the word 'GEOMETRY' are examples of well-defined sets, while sets based on subjective qualities like honesty or efficiency are not well-defined.
Step-by-step explanation:
When discussing well-defined sets, we refer to collections where it is clear whether an object belongs to the set or not, without any ambiguity or personal judgment. Among the options provided:
- (a) All the colors in the rainbow is a well-defined set because the colors can be clearly identified (red, orange, yellow, green, blue, indigo, and violet).
- (b) All the points that lie on a straight line is also a well-defined set, considering a particular straight line is specified, because every point can be precisely determined.
- (d) All the consonants of the English alphabet is a well-defined set, as there are exactly 21 consonants in the English alphabet, and each can be distinctly identified.
- (h) All the prime numbers less than 100 is a well-defined set since prime numbers are exactly definable and there is a finite list of them below 100.
- (i) All the letters in the word GEOMETRY is a well-defined set because the letters making up the word are specific and countable.
However, sets like all the honest members in the family, all the tall boys of the school, and all the efficient doctors of the hospital involve subjective judgments and are therefore not well-defined.