Determine whether each statement is true or false. {5, 8, 9} = {5, 8, 9, 0}

Verified step by step guidance

1. Understand the meaning of the equality of two sets: Two sets are equal if and only if they contain exactly the same elements.
2. List the elements of the first set: {5, 8, 9}.
3. List the elements of the second set: {5, 8, 9, 0}.
4. Compare the elements of both sets to see if every element in the first set is in the second set and vice versa.
5. Since the second set contains an extra element (0) that is not in the first set, conclude that the two sets are not equal.

Key Concepts

Set Equality

Two sets are equal if and only if they contain exactly the same elements. Order and repetition do not matter in sets; what matters is that every element of one set is in the other and vice versa.

Subset and Superset

A set A is a subset of set B if every element of A is also in B. Conversely, B is a superset of A. Understanding subsets helps determine if one set is contained within another, which is key to comparing sets.

Elements of a Set

Elements are the distinct objects contained in a set. Identifying and comparing these elements accurately is essential to determine relationships between sets, such as equality or subset relations.