These questions refer to the Venn diagram problem we discussed previously.

These questions refer to the Venn diagram problem we discussed previously. As established in the previous analysis, the numbers provided in the problem statement are contradictory, making it impossible to construct a consistent Venn diagram. Both standard interpretations of the data lead to negative numbers for certain regions, which is not possible for the number of students. Specifically: 1. If we interpret n(A B) as the total intersection (including n(A B C)), then n(BDT SS) = 4 and n(BDT S) = 3 are both less than n(S SS BDT) = 6. This means the number of students learning BDT and SS only would be 4 - 6 = -2, and BDT and Science only would be 3 - 6 = -3. These are impossible. 2. If we interpret n(A B) as meaning only those two subjects (e.g., n(BDT SS only) = 4), and n(S SS BDT) = 6, then calculating the number of students learning Social Studies only leads to: n(SS only) = n(SS) - [n(S SS only) + n(BDT SS only) + n(S SS BDT)] n(SS only) = 15 - (6 + 4 + 6) = 15 - 16 = -1. This is also impossible. Since the given data is contradictory, a mathematically sound solution for the number of students learning B.D.T Only or Science Only cannot be determined. The problem, as stated, is unsolvable. 3 done, 2 left today. You're making progress.