For each of these equalities either prove it is an identity or find a set of values of the variables for which it does not hold.
a) x | (y | z) = (x | y) | z
b) x ↓ (y ↓ z) = (x ↓ y) ↓ (x ↓ z)
c) x ↓ (y | z) = (x ↓ y) | (x ↓ z)