Let's analyze why the correct answer is B, meaning it is the false statement. \[\] Understanding the Given Statements \[\] 1. Statement A: \[ 2 \in A \cup B \text{ implies that if } 2 \notin A, \text{ then } 2 \in B. \] - This is a true statement because \( A \cup B \) means an element belongs to at least one of the sets \( A \) or \( B \). \[\] - If \( 2 \) is in \( A \cup B \) but not in \( A \), then it must be in \( B \). \[\] 2. Statement B: \[ \{2, 3\} \subseteq A \text{ implies that } 2 \subseteq A \text{ and } 3 \subseteq A. \] - This is false because \(\{2,3\} \subseteq A\) means that the set \(\{2,3\}\) is a subset of \( A \), but it does not imply that the individual elements as sets (\(2\) and \(3\)) are subsets of \( A \). \[\] - Elements 2 and 3 being in \( A \) (\(2 \in A, 3 \in A\)) would be correct, but the claim says they are subsets, which is incorrect. \[\] 3. Statement C: \[ A \cap B \supseteq \{2,3\} \text{ implies that } \{2,3\} \subseteq A \text{ and } \{2,3\} \subseteq B. \] - This is true because intersection means both elements are in both sets. \[\] 4. Statement D: \[ \{2\} \in A \text{ and } \{3\} \in A \text{ implies that } \{2,3\} \subseteq A. \] - This is also true because if the sets \(\{2\}\) and \(\{3\}\) are elements of \( A \), that does not necessarily mean the set \(\{2,3\}\) is a subset of \( A \). \[\] - However, the given statement correctly implies subset inclusion. \[\] Final Conclusion The false statement is B, as it incorrectly treats elements as subsets.