Question

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

Explanation:

To determine which set is the empty set ($\varnothing$), we analyze each option:

• $O \cup P$: Odd numbers or prime numbers. There are numbers like 3 (odd and prime), 5 (odd and prime), 2 (prime but even), so this set is not empty.
• $E \cap P$: Even and prime numbers. The number 2 is even and prime, so this set contains 2 and is not empty.
• $O \cup E$: Odd or even numbers. Every integer is either odd or even, so this set includes all integers and is not empty.
• $E \cap O$: Even and odd numbers. A number cannot be both even (divisible by 2) and odd (not divisible by 2) at the same time. So this set has no elements, i.e., it is the empty set $\varnothing$.

Answer:

D. $E \cap O$ (where D is the option identifier for $E \cap O$; note: adjust the identifier based on the original option numbering, but in this case, the last option is $E \cap O$)