Question

which of the following are true about x? check all that apply. \\(\square\\ x\
otin a\\) \\(\square\\ x\in b\\) \\(\square\\ x\
otin c\\) \\(\square\\ x\in a\cup b\\) \\(\square\\ x\in a\cup c\\) \\(\square\\ x\in a\cap b\\)

Explanation:

Step1: Analyze \( x

otin A \)
\( x \) is in the intersection of \( A \) and \( B \), so \( x \in A \). Thus, \( x
otin A \) is false.

Step2: Analyze \( x \in B \)

\( x \) is in the overlapping region of \( A \) and \( B \), so \( x \) is in \( B \). This is true.

Step3: Analyze \( x

otin C \)
\( x \) is not in the region of \( C \) (the green circle), so \( x
otin C \) is true.

Step4: Analyze \( x \in A \cup B \)

\( A \cup B \) includes all elements in \( A \) or \( B \). Since \( x \) is in both \( A \) and \( B \), \( x \in A \cup B \) is true.

Step5: Analyze \( x \in A \cup C \)

\( A \cup C \) includes elements in \( A \) or \( C \). \( x \) is in \( A \) (not in \( C \)), so \( x \in A \cup C \) is true.

Step6: Analyze \( x \in A \cap B \)

\( A \cap B \) is the intersection of \( A \) and \( B \), and \( x \) is in that overlapping region. So this is true.

Answer:

• \( x \in B \)
• \( x

otin C \)

• \( x \in A \cup B \)
• \( x \in A \cup C \)
• \( x \in A \cap B \)