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9 October, 17:44

How many different elements does A * B have if A has m elements and B has n elements?

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  1. 9 October, 18:03
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    Answer: mn

    Step-by-step explanation:

    A set refers to a well-defined collection of items.

    For example : Set of natural numbers (N)

    Set of rational numbers (Q).

    A Cartesian product is a product of two different sets.

    such as M = {1,2} and N={3,4}

    Then M x N = { (1,3), (1,4), (2,3), (2,4) }

    According to the properties of the Cartesian product of sets, if a set P has 'k' elements and an another set Q has 'r' elements, then the number of different elements in P x Q = kr

    Similarly, if A has m elements and B has n elements, then A x B has 'mn' elements.

    ∴ The number of ifferent elements does A * B have if A has m elements and B has n elements = mn
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