Question

Please help ASAP

Answer 1

Answer: See the diagram below

Specifically, refer to figure 4.

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The set U is the universal set. It represents every teacher. Let's draw this as a rectangle. Divide the rectangle so that one portion represents female teachers, and the other represents male teachers. I'll use a vertical line to divide the universal set.

Now draw a circle such that one portion of the circle is in the "male teacher" region and the other portion of the circle is in the "female teacher" region. Lastly, shade the region inside the circle that is also in the male teacher region. The diagram below shows the step by step process.

Figure 1 is the rectangle representing the universal set, which in this case is the set of all teachers.

Figure 2 splits up set U into female teachers on the left and male teachers on the right.

Figure 3 adds a circle, set M, to represent all math teachers. This circle spans the male and female teacher regions, since we can have either male or female math teachers.

Figure 4 adds labels A,B,C,D such that

• A = set of female teachers that don't teach math
• B = set of female teachers that teach math
• C = set of male teachers that teach math. This region is highlighted to answer the question your teacher provided.
• D = set of male teachers that don't teach math

There are no gaps or overlaps between any of the A,B,C,D regions. We consider these regions to be mutually exclusive. If a person is in region B for instance, then they cannot be in any other region. This is assuming no person teaches more than one subject. Note how regions A,B,C,D completely fill the set U, and do so without any gaps or overlaps. So we can say that set U is partitioned into those four regions.