Question

Let ( A={1,2.3} ). Decide if each set below is or is not equal to ( A ). A ( {3,2,1} ) A ( {1,1,2,3} ) A ( {1,2,3,4} ) A ( {3,2,1,2,2} )

Answer 1

In set theory, two sets are equal if they contain exactly the same elements, regardless of order or repetition. Sets {3,2,1}, {1,1,2,3}, and {3,2,1,2,2} are equal to set A, while {1,2,3,4} is not.

Step-by-step explanation:

The student is asking about the concept of set equality in mathematics. For two sets to be equal, they must contain the exact same elements and no others. Repetition of elements does not matter in set theory, nor does the order in which they are listed.

• Set {3,2,1} is equal to set A because it contains the same elements as A, namely 1, 2, and 3.
• Set {1,1,2,3} is also equal to set A because repetition is irrelevant in sets, and it contains exactly the elements of A.
• Set {1,2,3,4} is not equal to set A because it contains an extra element (4) that is not in A.
• Set {3,2,1,2,2} is equal to set A because again, repetition is irrelevant, and the unique elements match those in A.