Let A be the set of patients who have Hypertension, B be the set of patients who have Diabetes, and C be the…

Question

Let A be the set of patients who have Hypertension, B be the set of patients who have Diabetes, and C be the set of patients who have High Cholesterol. D is the set of patients older than 65 years. De

ScanSolve AI Tutor · Accepted Answer

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 Δ B represents the set of patients who have Hypertension or Diabetes, but not both. Step 2: Explain what |A Δ B| represents. |A Δ 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

Let A be the set of patients who have Hypertension, B be the set of patients who have Diabetes, and C be the set of patients who have High Cholesterol. D is the set of patients older than 65 years. De

Step-by-step solution

Part a(i)· 1 step

Identify the medical condition.

Part a(ii)· 2 steps

Describe $(A \cup B) \cap D$ .

Explain its relevance to public health planning.

Part a(iii)· 1 step

Describe the patients in $B'$ .

Part a(iv)· 2 steps

Describe $A \cap C'$ .

Identify the key difference.

Part a(v)· 1 step

Combine using set notation.

Part a(vi)· 1 step

Explain what $|A \Delta B|$ represents.

Part a(vii)· 1 step

Express using set notation.

Part a(viii)· 1 step

List all possible subsets of $D$ .

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More Mathematics Questions

Let A be the set of patients who have Hypertension, B be the set of patients who have Diabetes, and C be the set of patients who have High Cholesterol. D is the set of patients older than 65 years. De

Step-by-step solution

Part a(i)· 1 step

Identify the medical condition.

Part a(ii)· 2 steps

Describe (A∪B)∩D(A \cup B) \cap D(A∪B)∩D.

Explain its relevance to public health planning.

Part a(iii)· 1 step

Describe the patients in B′B'B′.

Part a(iv)· 2 steps

Describe A∩C′A \cap C'A∩C′.

Identify the key difference.

Part a(v)· 1 step

Combine using set notation.

Part a(vi)· 1 step

Explain what ∣AΔB∣|A \Delta B|∣AΔB∣ represents.

Part a(vii)· 1 step

Express using set notation.

Part a(viii)· 1 step

List all possible subsets of DDD.

Still stuck on this one?

More Mathematics Questions

Describe $(A \cup B) \cap D$ .

Describe the patients in $B'$ .

Describe $A \cap C'$ .

Explain what $|A \Delta B|$ represents.

List all possible subsets of $D$ .