Sets

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Solution: (i) NOT a set - The criterion 'most talented' is subjective and varies from person to person. No well-defined rule to decide membership. (ii) IS a set - An even integer is clearly defined as…

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Solution: Step 1: Identify the condition: x is a natural number AND 3 < x ≤ 10. Step 2: Find natural numbers greater than 3 and less than or equal to 10. Step 3: List them: 4, 5, 6, 7, 8, 9, 10. There…

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Solution: Step 1: Analyze the pattern in the set: 1 = 1³, 8 = 2³, 27 = 3³, 64 = 4³, 125 = 5³. Step 2: Recognize that each element is a perfect cube of natural numbers. Step 3: Identify that elements c…

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Solution: Step 1: Identify what the set contains: All prime numbers less than 1000. Step 2: Consider: Can we count all primes less than 1000? Yes, there is a definite upper limit (1000). Step 3: The s…

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Solution: Step 1: Solve the equation in set A: x² - 5x + 6 = 0. Step 2: Factor: (x - 2)(x - 3) = 0. Step 3: Find solutions: x = 2 or x = 3. Step 4: Therefore A = {2, 3}. Step 5: Compare: A = {2, 3} an…

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Solution: Step 1: Check if every element of A is in B. Step 2: 1 ∈ A and 1 ∈ B ✓, 2 ∈ A and 2 ∈ B ✓, 3 ∈ A and 3 ∈ B ✓. Step 3: All elements of A are in B, so A ⊂ B. Step 4: Check if A = B: B contains…

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Solution: Step 1: Recall: A ∪ B includes all elements from A and all elements from B, with common elements listed only once. Step 2: List elements of A: 1, 3, 5, 7. Step 3: List elements of B: 3, 5, 9…

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Solution: Step 1: Find all divisors of 24: A = {1, 2, 3, 4, 6, 8, 12, 24}. Step 2: Find all divisors of 36: B = {1, 2, 3, 4, 6, 9, 12, 18, 36}. Step 3: Find common divisors (elements in both A and B):…