How to solve a three set problem
Give a specific example.
38 student are in a class 16 like yam,6 like kenkey only,9 like plantain only and 2 likes both the three foods
To solve a three-set problem, you need to understand the problem statement and determine the relationship between the sets. Here is a step-by-step guide on how to approach and solve a three-set problem:
1. Read and understand the problem statement: Carefully read the problem to grasp the information provided and the required outcome.
2. Identify the given sets: Identify the three sets mentioned in the problem, and assign labels to each set. For example, let's say we have sets A, B, and C.
3. Analyze the relationship between the sets: Determine how the sets are related to each other. There are different possible relationships, including intersections, unions, complements, and subsets.
4. Use the appropriate set operation: Select the correct set operation that matches the given relationship between the sets:
a. Union (U): If the problem requires finding the elements that belong to any of the three sets, you need to perform the union operation. Symbolically, A U B U C represents all the elements that belong to sets A, B, or C.
b. Intersection (∩): If the problem requires finding the elements that are common to all three sets, you need to perform the intersection operation. Symbolically, A ∩ B ∩ C represents the elements that belong to all three sets.
c. Complement ('): If the problem mentions the complement of a set, it refers to the elements that do not belong to that set. The complement of set A is represented by A'.
d. Subset (⊆): If the problem involves identifying whether one set is a subset of another, check if all the elements of set A are also present in set B. In this case, A is said to be a subset of B (A ⊆ B).
5. Perform the necessary operations: Apply the identified set operations to the given problem and calculate the desired outcome. Be mindful of the specific set operation required to solve the problem.
6. Verify and interpret the solution: Double-check your solution to ensure all steps were followed correctly. Interpret the solution in terms of the problem statement. For example, if you were asked to find the common elements between sets A, B, and C, provide the answer in the form of a list or set of elements.
Remember, each problem may have its unique approach and requirements. Being familiar with set theory and the various operations will help you determine which operation to use and how to tackle the problem effectively.