This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Abba, good to see you again. Here are the solutions for question 1: a) i) Step 1: Define A B. A B represents the set of patients who have Hypertension or Diabetes (or both). Step 2: Identify the medical condition. This group represents patients with at least one of Hypertension or Diabetes. ii) Step 1: Define the sets involved. A B represents patients with Hypertension or Diabetes. D represents patients older than 65 years. Step 2: Describe (A B) D. (A B) D represents patients who have Hypertension or Diabetes AND are older than 65 years. Step 3: Explain its relevance to public health planning. In public health planning, this set represents elderly patients with at least one of Hypertension or Diabetes. This group is a high-risk population that may require targeted healthcare interventions and resource allocation. iii) Step 1: Define B'. B' is the complement of set B. Step 2: Describe the patients in B'. The patients in set B' are those who do not have Diabetes. iv) Step 1: Describe A - C. A - C represents patients who have Hypertension but do not have High Cholesterol. Step 2: Describe A C'. C' represents patients who do not have High Cholesterol. A C' represents patients who have Hypertension AND do not have High Cholesterol. Step 3: Identify the key difference. The key difference is that A - C and A C' are two different notations for the exact same set of patients. They represent the same group. v) Step 1: Identify the conditions. Patients who have Diabetes are in set B. Patients who do not have High Cholesterol are in set C'. Step 2: Combine using set notation. The set notation is B C' or B - C. vi) Step 1: Define symmetric difference in words. The symmetric difference A B represents the set of patients who have Hypertension or Diabetes, but not both. Step 2: Explain what |A B| represents. |A B| represents the number of patients who have Hypertension or Diabetes, but not both. vii) Step 1: Identify the conditions for "exactly one". A patient has exactly one condition if they have A but not B and not C, OR B but not A and not C, OR C but not A and not B. Step 2: Express using set notation. The set of patients is (A B' C') (B A' C') (C A' B'). viii) Step 1: List the elements of set D. D = \Fever, Cough\ Step 2: List all possible subsets of D. The power set P(D) is: P(D) = \, \Fever\, \Cough\, \Fever, Cough\\ Send me the next one 📸