Final answer:
The mother in the sentence strongly dislikes laziness and is vehemently against sleeping in on Sundays.
Step-by-step explanation:
The correct answer is b) detested. In the given sentence, the phrase 'Her mother _______ laziness of any kind and railed vehemently against sleeping in on Sundays' indicates that the mother strongly dislikes laziness and is strongly against sleeping in on Sundays. The word 'detested' means to strongly dislike or hate, which accurately conveys the mother's feelings. The other options, 'appreciated', 'embraced', and 'dismissed', do not fit the context and meaning of the sentence. Therefore, the correct option is 'b) detested'.