Answer:
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
