Question

and venn diagrams
the venn diagram shows three types of numbers: odd (o), even (e), and prime (p).
which is represented by ∅?
o ∪ e
e ∩ o
o ∪ p
e ∩ p

Explanation:

Step1: Recall Set Operations

• Union ($\cup$): Elements in either set.
• Intersection ($\cap$): Elements in both sets.
• Empty set ($\varnothing$): No elements.

Step2: Analyze Each Option

• Option 1: \( O \cup E \)

Odd or even numbers. All integers are either odd or even, so \( O \cup E \) is all integers (not empty).

• Option 2: \( E \cap O \)

Numbers that are both even and odd. A number can’t be both, so \( E \cap O = \varnothing \).

• Option 3: \( O \cup P \)

Odd or prime numbers. Many numbers (e.g., 3, 5, 7) are odd and prime; 2 is prime (even), so this set has elements (not empty).

• Option 4: \( E \cap P \)

Even and prime numbers. The number 2 is even and prime, so \( E \cap P = \{2\} \) (not empty).

Answer:

\( \boldsymbol{E \cap O} \) (the second option)