Question

in the venn diagram, let u be the set of all 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? 14 11 17 8

Explanation:

Step1: Identify regions in Painting

The Painting circle has three regions: only Painting (8), intersection with Chorus (3), and intersection with Theater (4), and the triple intersection (2). Wait, no, wait. Wait, the Venn diagram: Painting circle includes the part only in Painting (8), the part in Painting and Chorus (3), the part in Painting and Theater (4), and the part in all three (2)? Wait, no, let's check again. Wait, the Chorus circle: 7 (only Chorus), 3 (Chorus and Painting only), 16 (Chorus and Theater only), 2 (all three). Painting circle: 3 (Chorus and Painting only), 8 (only Painting), 4 (Painting and Theater only), 2 (all three). So to find total in Painting, we add all regions in the Painting circle: only Painting (8) + Chorus and Painting (3) + Painting and Theater (4) + all three (2)? Wait, no, wait the numbers: 3 (Chorus-Painting only), 8 (only Painting), 4 (Painting-Theater only), and 2 (all three). Wait, no, maybe I misread. Wait the diagram: Chorus has 7 (only), 3 (Chorus-Painting), 16 (Chorus-Theater), 2 (all three). Painting has 3 (Chorus-Painting), 8 (only Painting), 4 (Painting-Theater), 2 (all three). So total in Painting is 3 + 8 + 4 + 2? Wait 3+8=11, 11+4=15, 15+2=17? Wait no, wait the options are 14,11,17,8. Wait maybe I misread the regions. Wait let's look again: the Painting circle: the parts are: 3 (overlap with Chorus only), 8 (only Painting), 4 (overlap with Theater only), and 2 (overlap with both Chorus and Theater). Wait, no, the triple overlap is 2, so the regions in Painting are: only Painting (8), Chorus-Painting only (3), Painting-Theater only (4), and all three (2). So sum them: 3 + 8 + 4 + 2 = 17? Wait but let's check again. Wait the Chorus circle: 7 (only), 3 (Chorus-Painting), 16 (Chorus-Theater), 2 (all three). Theater circle: 9 (only), 16 (Chorus-Theater), 4 (Painting-Theater), 2 (all three). Painting circle: 3 (Chorus-Painting), 8 (only), 4 (Painting-Theater), 2 (all three). So yes, total in Painting: 3 (Chorus-Painting) + 8 (only) + 4 (Painting-Theater) + 2 (all three) = 3+8=11, 11+4=15, 15+2=17. Wait but the options have 17 as one of them. Wait but maybe I made a mistake. Wait another way: maybe the 3 is Chorus-Painting only, 8 is only Painting, 4 is Painting-Theater only, and 2 is all three. So 3+8+4+2=17. So the answer should be 17.

Step2: Sum the regions in Painting

To find the total number of students in the Painting class, we add all the regions that are part of the Painting circle. These regions are:

• Only Painting: \( 8 \)
• Chorus and Painting only: \( 3 \)
• Painting and Theater only: \( 4 \)
• All three (Chorus, Painting, Theater): \( 2 \)

Summing these values: \( 3 + 8 + 4 + 2 = 17 \).

Answer:

17