Question

in the venn diagram, consider u = {students in 10th grade at lee high school}. the diagram shows the electives chosen by the students in the 10th grade. how many students chose to participate in the painting class? 8 11 14 17

Explanation:

Step1: Identify regions in Painting circle

The Painting circle has three regions: only Painting (8), intersection with Chorus (3), intersection with Theater (4), and intersection with both Chorus and Theater (2)? Wait, no—wait, in a three - set Venn diagram, the regions for Painting are: only Painting, Painting and Chorus only, Painting and Theater only, and all three (Chorus, Painting, Theater) intersection. Wait, looking at the diagram: the Painting circle has 8 (only Painting), 3 (Painting and Chorus only), 4 (Painting and Theater only), and 2 (all three). Wait, no, actually, to find the total number of students in Painting, we need to sum all the regions that are part of the Painting circle.

Step2: Sum the regions in Painting

The regions in the Painting circle are: 8 (only Painting), 3 (Painting ∩ Chorus only), 4 (Painting ∩ Theater only), and 2 (Painting ∩ Chorus ∩ Theater). Wait, no, wait the diagram: let's check again. The Painting circle: the parts are 8 (only Painting), 3 (Chorus and Painting only), 2 (all three), and 4 (Painting and Theater only). So we sum these: 8 + 3+ 2 + 4. Wait, 8 + 3 is 11, 11+2 is 13, 13 + 4 is 17? Wait no, maybe I misread. Wait the Venn diagram: Chorus has 7 (only Chorus), 3 (Chorus and Painting only), 16 (Chorus and Theater only), 2 (all three). Theater has 9 (only Theater), 16 (Chorus and Theater only), 4 (Painting and Theater only), 2 (all three). Painting has 8 (only Painting), 3 (Chorus and Painting only), 4 (Painting and Theater only), 2 (all three). So to find the total number of students in Painting, we add the regions that are inside the Painting circle: only Painting (8), Chorus and Painting only (3), Painting and Theater only (4), and all three (2). So 8+3 + 4+2. Let's calculate: 8 + 3 = 11, 11+4 = 15, 15 + 2 = 17? Wait no, wait maybe the regions are: only Painting (8), Painting and Chorus (3), Painting and Theater (4), and all three (2). Wait, no, in a Venn diagram with three sets (Chorus, Painting, Theater), the Painting circle's total is the sum of: only Painting, Painting ∩ Chorus only, Painting ∩ Theater only, and Painting ∩ Chorus ∩ Theater. So from the diagram, only Painting is 8, Painting ∩ Chorus only is 3, Painting ∩ Theater only is 4, and all three is 2. So 8+3 + 4+2 = 17? Wait but let's check again. Wait the numbers: 8 (only Painting), 3 (Chorus and Painting), 2 (all three), 4 (Painting and Theater). So 8+3 + 2+4 = 17.

Answer:

17