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    Question

    If sets A and B contain 4 and 5 elements respectively,

    then the total number of binary relations from A to B is:
    A 2⁹ Correct Answer Incorrect Answer
    B 2²⁰ Correct Answer Incorrect Answer
    C 2¹⁰ Correct Answer Incorrect Answer
    D 2⁴⁵ Correct Answer Incorrect Answer

    Solution

    We are given:

    • Set A has 4 elements
    • Set B has 5 elements
    We are asked to find the total number of binary relations from A to B. A binary relation from A to B is a subset of the Cartesian product A × B.
    • Number of elements in A × B = 4 × 5 = 20
    • Each subset of A × B defines a binary relation ⇒ So total number of relations = Number of subsets of A × B = 2²⁰

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