Question

Let \(A\) be the set of students who live within one mile of school and let \(B\) be the set of students who walk to classes. Describe the students in each of these sets.

(a)\(A \cap B\)

(b)\(A \cup B\)

(c) \(A - B\)

(d) \(B - A\)

Short answer

(a) the set of students who live within 1 mile of school and who walk to classes.

(b) the set as the set of students who live within 1 mile of school or who walk to classes (or who do both).

(c) the set as the set of students who live within 1 mile of school but not walk to classes.

(d) the set of students who walk to classes but live more than 1 mile away from school

Step-by-step solution

Students’ describes in the set \(A \cap B\).

The given set for the students is:

\(A \cap B\)

The set is intersection of \(A\) and \(B\).

Students’ describes in the set as the set of students who live within 1 mile of school and who walk to classes.

Hence, the set of students who live within 1 mile of school and who walk to classes.

Students’ describes in the set \(A \cup B\).

The given set for the students is:

\(A \cup B\)

The set is union of \(A\) and \(B\).

Students’ describes in the set as the set of students who live within 1 mile of school or who walk to classes (or who do both).

Hence, the set as the set of students who live within 1 mile of school or who walk to classes.(or who do both).

Students’ describes in the set \(A - B\).

The given set for the students is:

\(A - B\)

The set is difference of \(A\) and \(B\).

Students’ describes in the set as the set of students who live within 1 mile of school but not walk to classes.

Hence, the set as the set of students who live within 1 mile of school but not walk to classes.

Students’ describes in the set \(B - A\).

The given set for the students is:

\(B - A\)

The set is difference of \(B\) and \(A\).

Students’ describes in the set as the set of students who walk to classes but live more than 1 mile away from school.

Hence, the set as the set of students who walk to classes but live more than 1 mile away from school.