The Venn diagram shows three types of numbers: odd (O), even (E), and prime (P).

Question

Circles O and P overlap, and circle P also overlaps with circle E.

Which is represented by Ø?

O ⋃ P
E ∩ P
O ⋃ E
E ∩ O

Answer 1

In the context of the Venn diagram you described, the symbol Ø typically represents the empty set, which includes no elements.

To interpret the options provided:

1. O ⋃ P: This represents the union of odd and prime numbers. It includes all numbers that are either odd or prime (or both). This set is not empty, as there are odd prime numbers (e.g., 3, 5, 7).

2. E ∩ P: This represents the intersection of even and prime numbers. The only even prime number is 2, so this set is not empty.

3. O ⋃ E: This represents the union of odd and even numbers. Since every integer is either odd or even, this set contains all integers, and thus is not empty.

4. E ∩ O: This represents the intersection of even and odd numbers. As no number can be both even and odd, this set is empty (Ø).

Therefore, Ø is represented by E ∩ O.