Select the Venn Diagram that best represents the relationship between the following classes.
Animals, Dogs, Cow
To solve this problem, we need to understand the hierarchical relationship between the classes: Animals, Dogs, and Cow. Animals are a broad category that includes all living creatures, including Dogs and Cows. Dogs and Cows are distinct categories within Animals, meaning they do not overlap.
Option B correctly represents this relationship. It shows two smaller circles (Dogs and Cows) inside a larger circle (Animals), with no overlap between the smaller circles.
Correct Option: B) The diagram shows two distinct circles within a larger circle, accurately representing Dogs and Cows as subsets of Animals.
Select the Venn Diagram that best represents the relationship between the following classes.
Crayons, Books, Stationary
To determine the correct Venn Diagram, we need to understand the relationship between the classes: Crayons, Books, and Stationary. The goal is to identify how these classes overlap or are distinct from each other.
Option A shows two smaller circles within a larger circle. This represents 'Crayons' and 'Books' as distinct entities within the larger category of 'Stationary'.
Correct Option: A) This option correctly represents 'Crayons' and 'Books' as separate entities within the larger 'Stationary' category.
Among 100 people, 40 people like tea while 58 people like coffee and 26 people like both tea and coffee. How many persons like neither tea nor coffee ?
This problem can be solved using the principle of inclusion-exclusion for two sets. We are given the total number of people, the number of people who like tea, the number of people who like coffee, and the number of people who like both. We need to find the number of people who like neither tea nor coffee.
Using the principle of inclusion-exclusion for two sets:
\[ N(T \cup C) = N(T) + N(C) - N(T \cap C) \]The number of people who like neither is the total number of people minus the number of people who like at least one beverage.
\[ \text{Neither} = N - N(T \cup C) \]\[ \text{Neither} = 100 - 72 \]\[ \text{Neither} = 28 \]A) 28 is the correct answer. This is the number of people who like neither tea nor coffee, calculated by subtracting the number of people who like at least one beverage from the total number of people.
Select the Venn Diagram that best represents the relationship between the following classes.
Dictionary, Books, Keyboard
To solve this question, we need to identify the logical relationships between the classes "Dictionary," "Books," and "Keyboard." A dictionary is a type of book, but a keyboard is unrelated to both dictionaries and books. We will use Venn diagrams to visualize these relationships.
Correct Option: C) The diagram shows one circle inside another (representing dictionaries within books) and a separate circle (representing keyboards), which accurately represents the relationships.
Select the Venn Diagram that best represents the relationship between the following classes.
Hours, Days, Year
To determine the correct Venn Diagram, we need to understand the hierarchical relationship between hours, days, and years. Each class is a subset of the next larger class.
Correct Option: B) The diagram with three nested circles correctly represents the relationship where hours are part of days, and days are part of years.
Select the Venn Diagram that best represents the relationship between the following classes.
Father, Mother, Family
The question asks us to identify the Venn Diagram that best represents the relationship between the classes: Father, Mother, and Family. The key is to understand how these categories relate to each other in terms of set theory.
Correct Option: A) This option accurately represents the relationship where "Father" and "Mother" are part of the "Family."
