Question

Your class is in groups, working on a sets worksheet. Your classmate suggests that if the union of two non-empty sets is the empty set, then the sets must be disjoint. What would you say to explain how this statement is false, and how would you help correct them

Answer 1

Answer:

The answer is "$\bold{A \cap\ B=\phi}$"

Explanation:

let

$A=\{1,2,3\}\\\\B=\{4,5,6\}$

A and B are disjoint sets and they are not an empty set  then:

$A\cup\ B=\{1,2,3,4,5,6\} \\\\A\cup\ B\neq 0$

therefore if the intersection of the two non-empty sets is the empty set then its disjoint set, which is equal to $\bold{A \cap\ B=\phi}$.