Are the Following Sets Equal?
| Set | Roster Form |
|---|---|
| \[ A=\{x:x \text{ is a letter in the word “reap”}\} \] | \[ A=\{r,e,a,p\} \] |
| \[ B=\{x:x \text{ is a letter in the word “paper”}\} \] | \[ B=\{p,a,e,r\} \] |
| \[ C=\{x:x \text{ is a letter in the word “rope”}\} \] | \[ C=\{r,o,p,e\} \] |
Conclusion
Since \[ A=\{r,e,a,p\} \] and \[ B=\{p,a,e,r\}, \] both have the same elements.
Therefore,
\[ A=B \]
But \[ C=\{r,o,p,e\} \] contains \[ o \] instead of \[ a. \]
Hence,
\[ \boxed{A=B\ne C} \]