The sets given are:

• $A = \{9, 10, 11, 12, 13\}$
• $B = \{8, 9, 10, 11, 12\}$

1. Are the sets equal?

Sets are considered equal if they have exactly the same elements. In this case:

• Set $A$ contains: 9, 10, 11, 12, 13
• Set $B$ contains: 8, 9, 10, 11, 12

Since set $A$ has the element 13, and set $B$ has the element 8 (which are not common), the sets are not equal. The correct answer is No.

2. Are the sets equivalent?

Sets are considered equivalent if they have the same number of elements, regardless of the actual elements themselves. Here, both sets have 5 elements:

• Set $A$ has 5 elements: {9, 10, 11, 12, 13}
• Set $B$ has 5 elements: {8, 9, 10, 11, 12}

Since both sets have the same number of elements, they are equivalent. The correct answer is Yes.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the difference between subsets and supersets?
2. Can two sets be equivalent but not equal?
3. What is the difference between union and intersection of sets?
4. How do you determine if one set is a proper subset of another?
5. How is the cardinality of a set defined?

Tip: When comparing sets, remember that "equality" is about the elements themselves, while "equivalence" is about the number of elements!