Question

There are three novels on Keishas reading table: Scoop, light, and Lanark. On her next trip, she can choose to take some or none, but not all, of these novels. In the braces below, list all the possible sets of novels that Keisha can take. Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol ∅

Answer 1

Given:

The number of novels=3

Scoop, light and Lanark.

Condition is given that Keishas can choose to take some or none, but not all, of these novels.

Let,

A denote the novel Scoop.

B denote the novel Light.

C denote the novel Lanark.

1) Keishas dont choose any novel it is given by,

`N=\mleft\lbrace\emptyset\mright\rbrace`

2) Keishas choose 1 novel and it can any one from 3 novels.

`\begin{gathered} N_1=\mleft\lbrace A\mright\rbrace \\ N_2=\mleft\lbrace B\mright\rbrace \\ N_3=\mleft\lbrace C\mright\rbrace \end{gathered}`

3) Keishas choose 2 novel and it can any two from 3 novels.

`\begin{gathered} N_1=\lbrace A,B\rbrace \\ N_2=\lbrace A,C\rbrace \\ N_3=\lbrace C,B\rbrace \end{gathered}`

Hence, the list all the possible sets of novels that Keisha can take is,

`\mleft\lbrace\emptyset,\mleft\lbrace A\mright\rbrace,\mleft\lbrace B\mright\rbrace,\mleft\lbrace C\mright\rbrace,\mleft\lbrace A,B\mright\rbrace,\mleft\lbrace B,C\mright\rbrace,\mleft\lbrace A,C\mright\rbrace\mright\rbrace`