Question
Which of the following statements is not true? (A) A set and its complement do not contain the same elements. (B) The union of any set and the empty set is the empty set. (C) o is a subset of every set. (D) The set that represents the union of two sets will always include each element in either set.
Ask by Ramirez Li. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Statement (B) is not true.
Solution
Let's analyze each statement:
(A) A set and its complement do not contain the same elements.
This is true because by definition, the complement of a set contains precisely those elements that are not in the set.
(B) The union of any set and the empty set is the empty set.
This is not true. The union of any set A with the empty set is A itself, since the empty set doesn’t contribute any elements.
(C) o is a subset of every set.
Here "o" represents the empty set, and it is indeed a subset of every set. This statement is true.
(D) The set that represents the union of two sets will always include each element in either set.
This is a restatement of the definition of union, so it is true.
Therefore, the statement that is not true is (B).
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Simplify this solution Mind Expander
Let's dive into some fun facts! The statement that "The union of any set and the empty set is the empty set" is actually a big no-no! Instead, the union of any set with the empty set results in the original set itself—so close, yet so far! Now, on to sets and subsets! It's fascinating that the empty set, often denoted as {}, is indeed a subset of every set. This is because a subset is defined as a set where all its elements are contained in another set, and the empty set contains no elements at all. Isn't that mind-blowing?
