Question

a number cube has faces numbered 1 to 6.
what is true about rolling the number cube one time? select three options.
□ s = {1, 2, 3, 4, 5, 6}
□ if a is a subset of s, a could be {0, 1, 2}.
□ if a is a subset of s, a could be {5, 6}.
□ if a subset a represents the complement of rolling a 5, then a = {1, 2, 3, 4, 6}.
□ if a subset a represents the complement of rolling an even number, then a = {1, 3}.

Explanation:

Step1: Analyze the sample space

The sample space \(S\) for rolling a number - cube numbered \(1\) to \(6\) is \(S=\{1,2,3,4,5,6\}\). So the first option is correct.

Step2: Check the subset condition

A subset \(A\) of \(S\) must have elements that are all in \(S\). Since \(0
otin S\), the set \(A = \{0,1,2\}\) is not a subset of \(S\).

Step3: Check another subset

The set \(A=\{5,6\}\) has elements \(5\in S\) and \(6\in S\). So if \(A\) is a subset of \(S\), \(A\) could be \(\{5,6\}\).

Step4: Find the complement of rolling a \(5\)

The complement of an event \(E\) (in this case \(E = \{5\}\)) is \(S - E\). So \(A=S-\{5\}=\{1,2,3,4,6\}\).

Step5: Find the complement of rolling an even number

The set of even numbers in \(S\) is \(E=\{2,4,6\}\). The complement \(A = S - E=\{1,3,5\}\), not \(\{1,3\}\).

Answer:

\(\text{S = \{1, 2, 3, 4, 5, 6\}}\), \(\text{If A is a subset of S, A could be \{5, 6\}}\), \(\text{If a subset A represents the complement of rolling a 5, then A=\{1, 2, 3, 4, 6\}}\)