Determine whether each statement is true or false. {5, 7, 9, 19} ∩ {7, 9, 11, 15} = {7, 9}

Verified step by step guidance

1. Identify the symbol ∩, which represents the intersection of two sets. The intersection includes all elements that are common to both sets.
2. List the elements of the first set: {5, 7, 9, 19}.
3. List the elements of the second set: {7, 9, 11, 15}.
4. Compare the two sets to find common elements. The common elements between the two sets are 7 and 9.
5. Conclude that the intersection of the two sets, {5, 7, 9, 19} ∩ {7, 9, 11, 15}, is indeed {7, 9}. Thus, the statement is true.

Key Concepts

Set Intersection

Set intersection is a fundamental operation in set theory that identifies the common elements between two sets. For example, if we have two sets A and B, the intersection A ∩ B consists of all elements that are present in both A and B. Understanding this concept is crucial for determining the truth of statements involving multiple sets.

Set Notation

Set notation is a mathematical language used to describe sets and their relationships. It includes symbols such as braces { } to denote sets, and the intersection symbol (∩) to indicate the intersection of sets. Familiarity with set notation allows for clearer communication of mathematical ideas and is essential for interpreting statements about sets.

True or False Statements

True or false statements are assertions that can be evaluated for their validity. In the context of set theory, determining whether a statement about sets is true or false involves checking if the elements claimed to be in the intersection actually belong to both sets. This logical evaluation is a key skill in mathematical reasoning.