{0,1,2,2,2,1,, 0,0,0,0}={0,1,2}
True
False
Answer (1)
Simplify the set 0 , 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 , 0 to 0 , 1 , 2 by removing duplicate elements.
Compare the simplified set 0 , 1 , 2 with the set 0 , 1 , 2 .
Since the two sets are identical, the statement is true.
The final answer is T r u e .
Explanation
Understanding Sets The question asks whether the set 0 , 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 , 0 is equal to the set 0 , 1 , 2 . A set is a collection of distinct objects, without regard to order. Therefore, duplicate elements in a set are treated as a single element.
Simplifying the Set The set 0 , 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 , 0 contains the elements 0, 1, and 2, with some elements repeated. In set theory, repeated elements are counted only once. Therefore, we can simplify the set 0 , 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 , 0 to 0 , 1 , 2 .
Comparing the Sets Now, we compare the simplified set 0 , 1 , 2 with the set 0 , 1 , 2 . Since they are identical, the statement 0 , 1 , 2 , 2 , 2 , 1 , 0 , 0 , 0 , 0 = 0 , 1 , 2 is true.
Final Answer Therefore, the statement is True.
Examples
In computer science, sets are used to store unique elements, such as user IDs or product codes. Understanding set theory helps in designing efficient algorithms for data storage and retrieval, ensuring that each element is unique and easily accessible. For example, when managing a database of users, sets can be used to ensure that each user has a unique ID, preventing duplicates and ensuring data integrity. This concept is also applicable in various fields like statistics, cryptography, and data analysis, where unique data representation is crucial.
