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We know that the set of natural numbers is a subset of the integer numbers so the common elements of the sets are natural numbers that proves the set of natural numbers intersect with the set of integers numbers is equal to the set of natural numbers. But how can I prove this by taking elements from the sets? Can anyone help me?

Anna
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  • Why does the first sentence of your question not constitute an answer? $\mathbb{N}$ is a subset of $\mathbb{Z}$, and the intersection of any set $A$ with a set $B$ that contains $A$ is $A$, so $\mathbb{N}\cap\mathbb{Z}=\mathbb{N}$. What kind of answer are you looking for? – Kevin Long Mar 27 '18 at 19:10

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Translate to logical predicates: If you know $A\subseteq B$ then $x\in A\to x\in B$. Consequently $x\in A\leftrightarrow(x\in A\land x\in B)$. In other words $A=A\cap B$.

Hagen von Eitzen
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