CT 15: Reasoning (Venn Diagram ভেনচিত্র)

1) A Venn diagram represents three sets X, Y, and Z. If the cardinalities of the sets are |X|=10, |Y|=15, and |Z|=20, and each pair of sets intersects exactly twice, what is |X ∪ Y ∪ Z|?

2) Select the Venn diagram that best represents the relationship among the given set of classes:
Metals, Silver, Gold

3) In a school, 500 students study mathematics, 300 study physics, and 200 study both subjects. If there are 1000 students in total, how many students study neither subject?

4) In a survey, it was found that 70% of people like coffee, 50% like tea, and 30% like both. What percentage of people like either coffee or tea?

5) Which of the following Venn diagrams correctly represents the relationships among the classes:
Educated, Mothers, Employed

6) Select the Venn diagram that best illustrates the relationship between the three given classes.
School, Teacher, Student

7) In a survey of 100 students, 60 like chocolate, 50 like vanilla, and 20 like both. How many students like either only chocolate or only vanilla?

8) In a Venn diagram with sets P, Q, and R, which of the following represents the elements that are in P and Q but not in R?

9) In a logical Venn diagram, if set H represents people who speak Hindi, set E represents people who speak English, and set F represents people who speak French, which part of the diagram shows people who speak both Hindi and French but not English?

10) In a group of 200 people, 120 like cricket, 80 like football, and 60 like both cricket and football. How many people like either cricket or football or both?