Does the element $x=21$ belong to the set $\lbrace x \mid-1 \leq x \leq 12, x \in I \rbrace$?
True
False
Answer (2)
Analyze the given set: The set includes all integers x such that − 1 ≤ x ≤ 12 .
Check if x = 21 satisfies the condition − 1 ≤ x ≤ 12 .
Since 12"> 21 > 12 , the condition is not met.
Conclude that x = 21 does not belong to the set, so the answer is F a l se .
Explanation
Problem Analysis We need to determine if the number x = 21 belongs to the set of integers x such that $-1 − 1 ≤ x ≤ 12
Defining the Set The set includes all integers from − 1 to 12 , inclusive. This means the set is { − 1 , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } .
Checking the Condition We need to check if x = 21 falls within this range. Since 21 is an integer, we only need to check if it satisfies the inequality -1
\[-1 \leq x \leq 12\]
Substituting x=21 , w e g e t -1 − 1 ≤ 21 ≤ 12 This statement is false because 21 is greater than 12 .
Final Answer Therefore, x = 21 does not belong to the set { x ∣ − 1 ≤ x ≤ 12 , x ∈ I } .
Examples
Imagine you're setting up a game with specific age restrictions. If the game is designed for players aged -1 to 12 (inclusive), a 21-year-old wouldn't be eligible to play. This is similar to our problem, where we checked if the number 21 fits within the specified range of -1 to 12.
The integer x = 21 does not belong to the set { x ∣ − 1 ≤ x ≤ 12 , x ∈ I } because it does not satisfy the condition of being between -1 and 12. Thus, the answer is False.
;
