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Given set A = x | 1 <= x2 < 9 and set B = 0, 1, 2, 3, 4, find the intersection of A and B, assuming x represents integers.
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Step-by-step solution
4 stepsTo find the intersection of sets and , we first need to determine the elements of set .
Determine the elements of set .
Set is defined as . This inequality can be broken down into two parts:
For :
Taking the square root of both sides, we get , which simplifies to .
This means or .For :
Taking the square root of both sides, we get , which simplifies to .
This means .Combining these conditions, we need such that ( or ) AND ().
The values of that satisfy both conditions are:
or .Identify the integer elements of set .
Since set consists of integers and the options are sets of integers, we assume must be an integer.
For the interval , the integers are .
For the interval , the integers are .
So, the integer elements of set are .Find the intersection of set and set .
Set
Set
The intersection consists of elements that are present in both sets.
Comparing the elements, we find that 1 and 2 are common to both sets.
Therefore, .Select the correct option.
The calculated intersection is , which corresponds to option B.
The final answer is .
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