A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Select three options.
[tex]S={1,2,3,4,5,6,7,8}[/tex]
* If [tex]A[/tex] is a subset of [tex]S[/tex], [tex]A[/tex] could be [tex]{1,2,3}[/tex].
* If [tex]A[/tex] is a subset of [tex]S[/tex], [tex]A[/tex] could be [tex]{7,8,9}[/tex].
* If a subset A represents spinning a number less than 4, then [tex]A ={1,2,3,4}[/tex].
* If a subset [tex]A[/tex] represents the complement of spinning an odd number, then [tex]A={2,4,6,8}[/tex].
Answer (2)
A subset can only contain elements from the original set.
The complement of a set contains all elements not in the original set.
Statement 1 and Statement 4 are true.
The three correct options are: If A is a subset of S , A could be { 1 , 2 , 3 } ; If a subset A represents the complement of spinning an odd number, then A = { 2 , 4 , 6 , 8 } .
Explanation
Analyze the problem We are given a spinner with 8 equal sections, numbered 1 to 8. We need to identify three correct statements about subsets of the possible outcomes. Let's analyze each statement.
Evaluate Statement 1 Statement 1: If A is a subset of S , A could be {1,2,3}.
A subset contains elements from the original set. Since 1, 2, and 3 are all in S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } , this statement is TRUE.
Evaluate Statement 2 Statement 2: If A is a subset of S , A could be {7,8,9}.
For {7, 8, 9} to be a subset of S , all its elements must be in S . However, 9 is not in S . Therefore, this statement is FALSE.
Evaluate Statement 3 Statement 3: If a subset A represents spinning a number less than 4, then A = { 1 , 2 , 3 , 4 } .
The numbers less than 4 are 1, 2, and 3. The set should be {1, 2, 3}, not {1, 2, 3, 4}. Therefore, this statement is FALSE.
Evaluate Statement 4 Statement 4: If a subset A represents the complement of spinning an odd number, then A = { 2 , 4 , 6 , 8 } .
The odd numbers in S are {1, 3, 5, 7}. The complement of these numbers in S is all the numbers in S that are not odd, which is {2, 4, 6, 8}. Therefore, this statement is TRUE.
Identify the True Statements The three true statements are:
If A is a subset of S , A could be {1,2,3}.
If a subset A represents the complement of spinning an odd number, then A = { 2 , 4 , 6 , 8 } .
Examples
Understanding subsets and complements is crucial in probability and statistics. For example, if you're analyzing the outcomes of rolling a die, you might want to know the probability of rolling an even number (a subset) or the probability of not rolling a 1 (the complement of rolling a 1). These concepts help in calculating the likelihood of different events.
The true statements about the spinner are: 1) A subset A could be 1, 2, 3 , and 2) The complement of spinning an odd number is A = 2, 4, 6, 8 . Only these two statements are correct based on the criteria for subsets and complements.
;
