Demonstrate the validity of the following identities by means of truth tables:
(a) DeMorgan’s theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x' + y' + z'
(b) The distributive law: x + yz = ( x + y )( x + z )
(c) The distributive law: x(y + z) = xy + xz
(d) The associative law: x + (y + z) = (x + y) + z
(e) The associative law and x(yz) = (xy)z
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