第 11 类 RD Sharma 解决方案 - 第 1 章集 - 练习 1.1
问题 1. 集合和集合有什么区别？给出支持你答案的理由。
解决方案：
A collection represents a group of objects. Whereas well-defined collections are called sets. Only unique elements can be present in a set.
Example: The collection of good novels is not a set. But, if we consider Good Novels in Rohan’s bookshelf, then it is a set. As contains the defined books that Rohan considers good, whereas a collection of good novels might be subjective.
Thus, we can say that every set is a collection, but every collection is not necessarily a set. Only well-defined collections are sets.
问题 2. 以下哪些集合是集合？证明你的答案：
(i) 小于 50 的所有自然数的集合。
(ii) 印度优秀曲棍球运动员的集合。
(iii) 你班上所有女孩的集合。
(iv) 印度所有有才华的作家的集合。
(v) 数学难题集。
(vi) Munshi Prem Chand 的小说集。
(vii) 本章所有问题的集合。
(viii) 以字母 J 开头的一年中所有月份的集合。
(ix) 世界上最危险的动物的集合。
(x) 素数的集合。
解决方案：
(i) Yes, it’s a set. Since, there are well-defined natural number less than 50, so it is a set.
(ii) No, it’s not a set. Since, good hockey players in India can be subjective depending from person to person, so it is not a set.
(iii) Yes, it’s a set. Since, there are a well-defined number of girls in a class, so it is a set.
(iv) No, it’s not a set. Since, whether a writer is talented or not can be a subjective opinion varying from one person to another, so it is not a set.
(v) No, it’s not a set. Since, the term ‘difficult’ is not well-defined. A topic may be difficult for one person, but may not be difficult for another person.
(vi) Yes, it’s a set. Since, there is a definite collection of novels written by Munshi Prem Chand, so it is a set.
(vii) Yes, it’s a set. Since, the number of questions belonging to a specific chapter will be a definite quantity, so it is a set.
(viii) Yes, it’s a set. Since, a collection of all months of a year beginning with the letter J is a definite quantity, so it is a set.
(ix) No, it’s not a set. Since, the term ‘most dangerous’ is subjective and not well-defined, so it’s not a set.
(x) Yes, it’s a set. Since, the collections of prime integers is a definite quantity, so it’s a set.
问题 3. 如果 A = {0,1,2,3,4,5,6,7,8,9,10}，则在以下每个空格中插入适当的符号或：
(一) 4个……一个
(ii) -4……A
(iii) 12…..A
(iv) 9…..A
(v) 0……一个
(vi) -2……A
解决方案：
(i) 4 ……A
Since, 4 is present in set A,
Therefore, 4 ∈ A
(ii) -4……A
Since, -4 is not present in set A,
Therefore, -4 ∉ A
(iii) 12…..A
Since, 12 is not present in set A,
Therefore, 12 ∉ A
(iv) 9…..A
Since, 9 is present in set A,
Therefore, 9 ∈ A
(v) 0……A
Since, 0 is present in set A,
Therefore, 0 ∈ A
(vi) -2……A
Since, -2 is not present in set A,
Therefore, -2 ∉ A