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11 April, 16:03

Let E, F, and G be three events. Find expressions for the following events: a. Non of them occur. b. Both E and G occur but F does not occur. c. only E occur.

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  1. 11 April, 16:25
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    a. (E U F U G) '

    b. E n F (G') or EF (G')

    c. E n (F U G) ' or E (F U G) '

    Step-by-step explanation:

    The three events are E, F, G

    For this question, we'll make use of set notations

    U - > Union

    Example is A U B which means an occurrence that happens in either A or B

    n - > Intersection

    Example is A n B which means an occurrence that happens in A and B.

    It can also be written as AB

    ' - > Complement

    Example is A' which means an event where A doesn't occur.

    So, we'll move to the questions

    a. None of them occur.

    This means that;

    E doesn't occur

    F doesn't occur

    G doesn't occur.

    So, the notation is (E U F U G) '

    b. Both E and F occur but G doesn't occur

    This mean that

    E and F occur

    G didn't occur.

    The notation is E n F (G') or EF (G')

    c. Only E occur

    This means that E occur

    And Either F or G didn't occur

    The notation is, E n (F U G) ' or E (F U G) '
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