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: Identify sample space

The sample space \(S\) of rolling a 6-sided cube is all possible outcomes, so \(S = \{1, 2, 3, 4, 5, 6\}\).

Step2: Check valid subset 1

A subset of \(S\) can only contain elements from \(S\). \(\{0,1,2\}\) includes 0, which is not in \(S\), so this is invalid.

Step3: Check valid subset 2

\(\{5,6\}\) only contains elements from \(S\), so this is a valid subset.

Step4: Find complement of rolling 5

The complement of rolling a 5 is all outcomes that are not 5, so \(A = \{1, 2, 3, 4, 6\}\).

Step5: Find complement of even numbers

Even numbers in \(S\) are \(\{2,4,6\}\). Their complement is all odd numbers: \(\{1,3,5\}\), so the given set \(\{1,3\}\) is invalid.

Answer:

S = {1, 2, 3, 4, 5, 6}
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}.