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A number cube has faces numbered 1 to 6. What is true about rolling the number cube one time? Select three options.

1. If [tex]\( A \)[/tex] is a subset of [tex]\( S \)[/tex], [tex]\( A \)[/tex] could be [tex]\(\{5, 6\}\)[/tex].

2. If a subset [tex]\( A \)[/tex] represents the complement of rolling a 5, then [tex]\( A = \{1, 2, 3, 4, 6\} \)[/tex].

3. If a subset [tex]\( A \)[/tex] represents the complement of rolling an even number, then [tex]\( A = \{1, 3, 5\} \)[/tex].

(Note: [tex]\(\{0, 1, 2\}\)[/tex] is not a valid subset of [tex]\( S \)[/tex], because the number 0 is not on the cube.)

[tex]\[ S = \{1, 2, 3, 4, 5, 6\} \][/tex]

Sagot :

GinnyAnswer
Let's analyze each statement one-by-one to determine whether it is true or not.

1. Statement: If [tex]\(A \)[/tex] is a subset of [tex]\(S, A \)[/tex] could be [tex]\(\{0, 1, 2\}\)[/tex].

To be a subset of [tex]\(S = \{1, 2, 3, 4, 5, 6\}\)[/tex], every element in set [tex]\(A\)[/tex] must also be an element of set [tex]\(S\)[/tex]. The set [tex]\(\{0, 1, 2\}\)[/tex] includes the element 0, which is not in [tex]\(S\)[/tex].

Therefore, this statement is false.

2. Statement: If [tex]\(A\)[/tex] is a subset of [tex]\(S, A\)[/tex] could be [tex]\(\{5, 6\}\)[/tex].

To be a subset of [tex]\(S\)[/tex], every element in the set [tex]\(A\)[/tex] must also be an element of [tex]\(S\)[/tex]. The set [tex]\(\{5, 6\}\)[/tex] includes elements 5 and 6, both of which are in [tex]\(S\)[/tex].

Therefore, this statement is true.

3. Statement: If a subset [tex]\(A\)[/tex] represents the complement of rolling a 5, then [tex]\(A = \{1, 2, 3, 4, 6\}\)[/tex].

The complement of rolling a 5 means every possible outcome except rolling a 5. The set of all outcomes except 5 is [tex]\(\{1, 2, 3, 4, 6\}\)[/tex].

Therefore, this statement is true.

4. Statement: If a subset [tex]\(A\)[/tex] represents the complement of rolling an even number, then [tex]\(A = \{1, 3\}\)[/tex].

The even numbers in the set [tex]\(S = \{1, 2, 3, 4, 5, 6\}\)[/tex] are \{2, 4, 6\}. The complement of rolling an even number should include all outcomes that are not even numbers, thus it consists of the odd numbers. The odd numbers in the set are \{1, 3, 5\}.

Therefore, this statement is false.

To conclude, the statements that are true are:
- If [tex]\(A\)[/tex] is a subset of [tex]\(S\)[/tex], [tex]\(A\)[/tex] could be [tex]\(\{5, 6\}\)[/tex].
- If a subset [tex]\(A\)[/tex] represents the complement of rolling a 5, then [tex]\(A = \{1, 2, 3, 4, 6\}\)[/tex].

These are the steps and conclusions based on the analysis of each statement.
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