This question tests the inclusion-exclusion principle for finding the union of two sets. We need to find |T∪B|, the number of attendees who attended at least one session type. Using the formula |T∪B| = |T| + |B| - |T∩B|, we substitute the given values: |T∪B| = 110 + 95 - 40 = 165 attendees. This represents all attendees who attended either a technology session, a business session, or both. A common error would be to simply add 110 + 95 = 205, which double-counts the 40 attendees who attended both types of sessions.

This question tests set difference reasoning, specifically finding elements in one set but not another. We need students who play soccer but not basketball, which is |S| - |S∩B|. Given that |S| = 28 and |S∩B| = 10, the number of students who play only soccer is 28 - 10 = 18. This represents the portion of the soccer-playing students who are not in the intersection with basketball players. A common mistake would be to calculate |S| + |B| - |S∩B| = 28 + 24 - 10 = 42, which gives the total in either sport rather than just soccer alone.

This question tests Venn diagram reasoning for finding elements in exactly one set. We have 120 employees total, with |R| = 70, |F| = 55, and |R∩F| = 30. To find employees in exactly one set, we need those in R only plus those in F only. Employees in R only = 70 - 30 = 40, and employees in F only = 55 - 30 = 25. Therefore, employees in exactly one set = 40 + 25 = 65. A common mistake is to calculate |R∪F| = 70 + 55 - 30 = 95, which gives all employees in at least one set, not exactly one.

This question tests the inclusion-exclusion principle when given the union size directly. We need to find |R∩V| using the formula |R∪V| = |R| + |V| - |R∩V|. Substituting the given values: 120 = 98 + 64 - |R∩V|. Solving for the intersection: |R∩V| = 98 + 64 - 120 = 42. This represents the 42 members who both renewed their membership and volunteered. A common mistake would be to subtract the given values incorrectly or to confuse the union with the intersection when setting up the equation.

This question tests Venn diagram reasoning to find elements in exactly one set. We need to find employees who are in R but not T, plus those in T but not R. First, calculate |R only| = |R| - |R ∩ T| = 46 - 20 = 26 employees who work remotely but haven't completed training. Next, calculate |T only| = |T| - |R ∩ T| = 38 - 20 = 18 employees who completed training but don't work remotely. The total in exactly one set is 26 + 18 = 44. A common mistake would be to calculate |R ∪ T| = 64 instead, which includes those in both sets.

This question tests the inclusion-exclusion principle to find the intersection of two sets. We know 22 attended neither workshop, so |A∪B| = 110 - 22 = 88 attendees attended at least one workshop. Using inclusion-exclusion: |A∪B| = |A| + |B| - |A∩B|, we get 88 = 63 + 57 - |A∩B|. Solving for the intersection: |A∩B| = 63 + 57 - 88 = 32. This represents the 32 attendees who attended both workshops. A common mistake would be to add those who attended neither to the union calculation, giving an incorrect result.

This question tests finding a set's cardinality given partial information. We know 150 total households, 40 own neither pet, so 110 own at least one pet. We have |C| = 70 and |C ∩ O| = 25. Using |C ∪ O| = 110 and the inclusion-exclusion formula: 110 = 70 + |O| - 25. Solving for |O|: |O| = 110 - 70 + 25 = 65 households own a dog. A common error would be to calculate |O| = 110 - 70 = 40, forgetting to add back the intersection that was subtracted when finding the union.

This question tests set reasoning using the principle of inclusion-exclusion for two sets. We need to find the number of employees in neither set A (remote workers) nor set B (public transport users), which equals the total minus those in A∪B. Using the inclusion-exclusion principle: |A∪B| = |A| + |B| - |A∩B| = 46 + 38 - 19 = 65. Therefore, the number in neither set is 80 - 65 = 15. A common error would be to add |A| and |B| without subtracting the intersection, giving 84 employees in the union, which would incorrectly suggest -4 employees are in neither set.

This question tests set reasoning using the principle of inclusion-exclusion. We can model this with a Venn diagram where the universal set contains all 60 students, with two overlapping circles representing sets M (Math students) and P (Physics students). To find students studying at least one subject, we use |M ∪ P| = |M| + |P| - |M ∩ P| = 35 + 28 - 15 = 48. Therefore, the number of students studying neither subject is 60 - 48 = 12. A common error would be to add 35 + 28 = 63 without subtracting the overlap, which would incorrectly count the 15 students in both sets twice.

This question tests set theory reasoning using Venn diagrams for two overlapping sets. We model the students speaking French (F) and Spanish (S) with regions for only F, only S, and both. The union |F ∪ S| = 65 is given, so the intersection is 42 + 38 - 65 = 15. This allocates only French as 42 - 15 = 27 and only Spanish as 38 - 15 = 23. The result is justified by the inclusion-exclusion principle avoiding double-counting. A common incorrect option is 20, perhaps from subtracting the union from one set alone, like 42 + 38 - 80 = 0, but this ignores the given union and leads to errors.