## Related questions with answers

Let U = the universal set of all teachers in your school. Let the subsets of mathematics teachers, biology teachers, physics teachers, and chemistry teachers be represented by M, B, P, and C, respectively. Describe in words the following set, and name a teacher belonging to each set if such a teacher exists in your school.

a. $\bar{M} \cap \bar{B} \cap \bar{P} \cap \bar{C}$

b. $\overline{M \cup B \cup P \cup C}$

Solutions

VerifiedWe have to describe each of the given sets of a universal set $U$ that has all the teachers in our school. The subsets are those formed by mathematics $(M)$, physics $(P)$, biology $(B)$, and chemistry $(C)$ teachers.

*How do we denote a set with no elements?*

a.

$\overline{M}\cap\overline{B}\cap\overline{P}\cap\overline{C}$ is the set of teachers not belonging to M, and not belonging to B, and not belonging to P, and not belonging to C.

That is, the set of teachers that

$\text{\color{#c34632}{\bf do not teach} any of the subjects: maths, biology physics, or chemistry.}$

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