Question

If $Z$ is defined as the set of letters of the word $contract$, then the set can be represented in the Roster form as:

• A. $Z=\{c,o,n,t,r,a,m\}$
• B. $Z=\{c,o,n,t,r,a\}$
• C. $Z=\{a,n,t,r,c,o\}$
• D. $Z=\{c,o,n,r\}$

Answer 1

Answer: (B), (C)

$Z=\{a,n,t,r,c,o\}$

For Roster form of sets, we know that both the order and repitition of the elements is immaterial.

Hence, utilizing these two properties, we can represent the set as:
$Z=\{c,o,n,t,r,a\}$

Since order does not matter, we can also represent the set as: $Z=\{a,n,t,r,c,o\}$

Also, $Z\ne \{c,o,n,r\}$ as it does not contain all the letters of the word.