Find the union and the intersection of the sets $A=\{0,2,4,6,8,\cdots\}$ and $B=\{1,3,5,7,9,\cdots\}$.

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Lesson Parent: 
The Union and Intersection of Sets
Problem: 

Find the union and the intersection of the sets $A=\{0,2,4,6,8,\cdots\}$ and $B=\{1,3,5,7,9,\cdots\}$.

Answer: 

$A\cup B$ is the set of natural numbers and $A\cap B$ is the empty set.

SAMPLE SOLUTION

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Solution: 

The set $A$ is the set of all even natural numbers. The set $B$ is the set of all odd natural numbers.

The union of $A$ and $B$ is the set

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Therefore,

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In other words, <Sign in to see all the formulas> is the full set of natural numbers.

The intersection of $A$ and $B$ is the set

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There are no elements that are in both $A$ and $B$. Therefore, <Sign in to see all the formulas> is the empty set. (<Sign in to see all the formulas>.)