Does the element [tex]$p=60$[/tex] belong to the set [tex]$\lbrace p \mid p=3x, 0 \leq x \leq 21, x \in W\rbrace$[/tex]?
True
False
Answer (2)
Divide 60 by 3 to find the value of x: x = 3 60 = 20 .
Check if the value of x is within the given range: 0 ≤ 20 ≤ 21 .
Since 20 is a whole number and falls within the range, 60 belongs to the set.
Therefore, the answer is T r u e .
Explanation
Understanding the Problem We are given the set { p ∣ p = 3 x , 0 ≤ x ≤ 21 , x ∈ W } , where W represents the set of whole numbers. We want to determine if the number 60 belongs to this set. This means we need to find a whole number x such that 3 x = 60 and 0 ≤ x ≤ 21 .
Solving for x To find the value of x , we need to solve the equation 3 x = 60 . We can do this by dividing both sides of the equation by 3: x = 3 60 = 20 So, x = 20 .
Checking the Condition Now we need to check if the value of x we found satisfies the condition 0 ≤ x ≤ 21 . Since x = 20 , we have 0 ≤ 20 ≤ 21 , which is true. Therefore, 60 belongs to the set.
Conclusion Since we found a whole number x = 20 that satisfies both 3 x = 60 and 0 ≤ x ≤ 21 , we can conclude that 60 belongs to the set.
Examples
Imagine you are planning a school trip and need to figure out if you can divide the total cost equally among the students. If the total cost is $60 and each student needs to pay $3, you can use this math to determine if the number of students (x) can be a whole number between 0 and 21. In this case, x = 20, meaning 20 students can go on the trip, and each will pay $3, making the total cost $60.
The element p = 60 belongs to the set because it can be represented as 3 x where x = 20 , which is a whole number in the range 0 ≤ x ≤ 21 . Therefore, the answer is True .
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