Question

a spinner is divided into eight equal - sized sections, numbered from 1 to 8, inclusive. what is true about spinning the spinner one time? select three options. s = {1, 2, 3, 4, 5, 6, 7, 8} if a is a subset of s, a could be {1, 2, 3}. if a is a subset of s, a could be {7, 8, 9}. if a subset a represents spinning a number less than 4, then a = {1, 2, 3, 4}. if a subset a represents the complement of spinning an odd number, then a = {2, 4, 6, 8}.

Explanation:

Step1: Analyze the sample space

The spinner is numbered from 1 to 8. So the sample space \(S=\{1,2,3,4,5,6,7,8\}\). This option is correct.

Step2: Check subset \(A = \{1,2,3\}\)

Since \(1,2,3\in S\), \(A=\{1,2,3\}\) is a subset of \(S\). This option is correct.

Step3: Check subset \(A=\{7,8,9\}\)

Since \(9
otin S\), \(A = \{7,8,9\}\) is not a subset of \(S\). This option is incorrect.

Step4: Check subset \(A=\{1,2,3,4\}\) for numbers less than 4

Numbers less than 4 are 1,2,3. So \(A=\{1,2,3\}\), not \(\{1,2,3,4\}\). This option is incorrect.

Step5: Check complement of odd - numbered subset

Odd numbers in \(S\) are \(\{1,3,5,7\}\). The complement of this set (non - odd or even numbers) is \(\{2,4,6,8\}\). This option is correct.

Answer:

\(S = \{1,2,3,4,5,6,7,8\}\), If \(A\) is a subset of \(S\), \(A\) could be \(\{1,2,3\}\), If a subset \(A\) represents the complement of spinning an odd number, then \(A=\{2,4,6,8\}\)