Problem

Given sets $A, B, C$, and $U$, find the set $A-B$ using the listing method. \[ \begin{array}{l} A=\{1,4,6,7\} \\ B=\{0,1,4\} \\ C=\{5,7\} \\ U=\{0,1,2,3,4,5,6,7\} \end{array} \] \[ \mathrm{A}-\mathrm{B}=\{\square\} \] (Use a comma to separate answers as needed.)

Solution

Step 1 :The set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$.

Step 2 :So, we need to find the elements that are in set $A$ but not in set $B$.

Step 3 :The elements in set $A$ are $\{1,4,6,7\}$ and the elements in set $B$ are $\{0,1,4\}$.

Step 4 :Comparing these two sets, we see that the elements $1$ and $4$ are in both sets, so they are not included in the set difference $A - B$.

Step 5 :The elements $6$ and $7$ are in set $A$ but not in set $B$, so they are included in the set difference $A - B$.

Step 6 :Therefore, the set difference $A - B$ is $\{6,7\}$.

From Solvely APP
Source: https://solvelyapp.com/problems/31268/

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