Question

Determine whether each of these pairs of sets are equal.

1) 1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 1
2) 1, 1, 1
3) ∅, ∅

Answer 1

After examining the sets provided, the first pair is not equal because they contain different elements, while the second pair is equal because both are empty sets.

Step-by-step explanation:

The question involves understanding the concept of set equality. In mathematics, two sets are said to be equal if they contain exactly the same elements, without regard to order or repetition. Let's examine each pair of sets given:

• Set 1 contains the elements 1, 3, 5. The repetitions do not matter in set notation.
• Set 2 contains the element 1, with repetitions ignored.
• Set 3 contains no elements and is thus the empty set, denoted by ∅.

By comparing the sets:

• The first pair of sets (1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 3, 1) and (1, 1, 1) are not equal because the first one has elements 1, 3, and 5, while the second one only has the element 1.
• The second pair of sets (∅, ∅) are equal since both represent the empty set.