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    Question

    Let A = {10, 20, 30} and B = {5, 10, 15}. Which of the

    following relations from A to B is onto?
    A {(10, 5), (20, 10), (30, 5)} Correct Answer Incorrect Answer
    B {(10, 5), (20, 15), (30, 10)} Correct Answer Incorrect Answer
    C {(10, 15), (20, 10), (30, 10)} Correct Answer Incorrect Answer
    D {(10, 15), (20, 15), (30, 5)} Correct Answer Incorrect Answer

    Solution

    We are given two sets: A = {10, 20, 30} B = {5, 10, 15} We are to identify which relation from A to B is onto.   A relation R from A to B is onto (or surjective) if every element of B is the image of at least one element of A. In simple terms: Every element in B must appear as the second component in at least one ordered pair in the relation. Now check each option: (a) {(10, 5), (20, 10), (30, 5)} Elements of B used: 5, 10 15 is missing → Not onto (b) {(10, 5), (20, 15), (30, 10)} Elements of B used: 5, 10, 15 All elements of B are covered → This is onto (c) {(10, 15), (20, 10), (30, 10)} Elements of B used: 15, 10 5 is missing → Not onto (d) {(10, 15), (20, 15), (30, 5)} Elements of B used: 15, 5 10 is missing → Not onto Therefore, the correct answer is option (b).

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