If A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5}, how many ordered pairs (a, b) in A × B satisfy a² - b² = 0?
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Answer and explanation
Correct answer: 5
Factor the equation as a² - b² = (a - b)(a + b) = 0. Since a and b are both positive elements of {1,2,3,4,5}, the equation a + b = 0 is impossible. Therefore, a - b = 0, so a = b. The valid ordered pairs are (1,1), (2,2), (3,3), (4,4), and (5,5). There are exactly five such pairs, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Factor the equation as a² - b² = (a - b)(a + b) = 0. Since a and b are both positive elements of {1,2,3,4,5}, the equation a + b = 0 is impossible. Therefore, a - b = 0, so a = b. The valid ordered pairs are (1,1), (2,2), (3,3), (4,4), and (5,5). There are exactly five such pairs, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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