Does the element $x=1.5$ belong to the set {x |-1 \leq x \leq 12, x \in I}?
True
False
Answer (2)
Check if 1.5 satisfies the inequality − 1 ≤ x ≤ 12 .
Verify if 1.5 is an integer.
Since 1.5 is not an integer, it does not belong to the set.
Therefore, the answer is F a l se .
Explanation
Understanding the Problem We are given the set { x ∣ − 1 ≤ x ≤ 12 , x ∈ I } , where I represents the set of integers. We need to determine if the element x = 1.5 belongs to this set.
Checking the Inequality First, let's check if x = 1.5 satisfies the inequality − 1 ≤ x ≤ 12 . Since − 1 ≤ 1.5 ≤ 12 , the first condition is satisfied.
Checking for Integer Next, we need to check if x = 1.5 is an integer. Integers are whole numbers (without any fractional part). Since 1.5 has a fractional part (0.5), it is not an integer.
Conclusion Since x = 1.5 is not an integer, it does not belong to the set { x ∣ − 1 ≤ x ≤ 12 , x ∈ I } .
Examples
Imagine you are setting up a security system that only allows access to people with integer identification numbers. If someone tries to access the system with an ID of 1.5, they would be denied access because the system only recognizes whole numbers. This is similar to our problem, where only integers are allowed in the set, and 1.5 is not an integer.
The element x = 1.5 does not belong to the set because it is not an integer, even though it satisfies the given inequality. Therefore, the answer is False.
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