CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
If A = {x : x is a natural number and x² − 7x + 10 = 0}, how many subsets does A have?
Solving x² − 7x + 10 = 0 gives x = 2 and x = 5, so A has two elements. A set with n elements has 2ⁿ subsets, so A has 2² = 4 subsets, including the empty set and A itself.
- A2
- B4Correct
- C8
- D1
Explanation
x² − 7x + 10 = (x − 2)(x − 5) = 0, so x = 2 or 5, both natural numbers. A = {2, 5} has 2 elements, so the number of subsets is 2² = 4. Choosing 2 would count elements, not subsets.
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