dyGPTQuestion text{x| x ∈ Z, 0 ≤ x < 8} ⋂ {x| x ∈ R, 4 ≤ x < 16} is the set:a.{x| x ∈ R, 4 ≤ x < 8}b.{x| x ∈ Z, 0 ≤ x ≤ 8}c.{x| x ∈ Z, 0 ≤ x ≤16}d.{4, 5, 6, 7}
Question
dyGPTQuestion text
{x| x ∈ Z, 0 ≤ x < 8} ⋂ {x| x ∈ R, 4 ≤ x < 16} is the set:
a. {x| x ∈ R, 4 ≤ x < 8}
b. {x| x ∈ Z, 0 ≤ x ≤ 8}
c. {x| x ∈ Z, 0 ≤ x ≤ 16}
d. {4, 5, 6, 7}
Solution
The intersection of the two sets {x| x ∈ Z, 0 ≤ x < 8} and {x| x ∈ R, 4 ≤ x < 16} would be the set of all numbers that are common to both sets.
The first set includes all integers from 0 to 7, and the second set includes all real numbers from 4 to less than 16.
The common numbers between these two sets would be the integers from 4 to 7.
Therefore, the intersection of these two sets is {4, 5, 6, 7}, which corresponds to option d.
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