A number cube has faces numbered 1 to 6.

Question

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}.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}.

Answer 1

To determine the true statements about rolling a number cube with faces numbered from 1 to 6, let's analyze each option one by one:

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

   • This is true since the number cube has faces numbered from 1 to 6.

2. If A is a subset of S, A could be {0, 1, 2}:

   • This is false. {0, 1, 2} is not a subset of S = {1, 2, 3, 4, 5, 6} because it includes 0, which is not in S.

3. If A is a subset of S, A could be {5, 6}:

   • This is true. {5, 6} is a valid subset of S.

4. If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}:

   • This is true. The complement of rolling a 5 includes all other outcomes (1, 2, 3, 4, and 6).

5. If a subset A represents the complement of rolling an even number, then A = {1, 3}:

   • This is false. The even numbers in S are {2, 4, 6}, so the complement (the odd numbers) is {1, 3, 5}, not {1, 3}.

Based on this analysis, the three true statements are:

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