Question

which venn diagram correctly describes the relationship between the integers (i) and the natural numbers (n)?
first diagram: two separate circles labeled n and i, explanation because these two sets of numbers have no elements in common; second diagram: circle n with circle i inside, explanation because all integers are natural numbers; third diagram: circle i with circle n inside, explanation because all natural numbers are integers; fourth diagram: overlapping circles n and i, explanation because some integers are not natural numbers

Explanation:

Step1: Recall number set definitions

Natural numbers ($N$) are positive integers (e.g., $1, 2, 3, ...$). Integers ($I$) include all whole numbers: positive, negative, and zero (e.g., $... -2, -1, 0, 1, 2, ...$).

Step2: Analyze relationships

• First option: Wrong, as $N$ is a subset of $I$ (they share elements like $1,2,...$).
• Second option: Wrong, not all integers (e.g., $-1, 0$) are natural numbers.
• Third option: Correct, because every natural number is an integer (so $N$ is a subset of $I$).
• Fourth option: Wrong, the overlap is incomplete (all $N$ are $I$, so the $N$ circle should be entirely inside $I$).

Answer:

The Venn diagram with $N$ as a small circle inside $I$, labeled "because all natural numbers are integers".