Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.