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30 March, 02:25

Which of the following boolean algebra statements is true?

a) x & y = ~x | ~y

b) x | y | z = x & (y | z)

c) x | (y & z) = (x & y) | (x & z)

d) x & (y | z) = (x & y) | (x & z)

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  1. 30 March, 06:14
    0
    The only statement that is True is the d) x & (y | z) = (x & y) | (x & z)

    Explanation:

    The statement x & (y | z) = (x & y) | (x & z) satisfies the Distributive Law of Boolean Algebra that states:

    A & (B | C) = (A & B) | (A & C).

    You can also check that the others are False if you use the operation notation, lets see that any of the other statements are true:

    Statement a) x & y = ~x | ~y is equivalent to x * y=~x + ~y and this is False

    Statement b) x | y | z = x & (y | z) is equivalent to x + y + z = x * (y + z), by solving this you have x + y + z = x * y + x * z and those expressions are not the same, so is False

    For Statement c) x | (y & z) = (x & y) | (x & z) we have that this one does not satisfies the Distributive Law, therefore is False
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