Simplify each of the following Boolean expressions as much as possible using identities:

XY + (1 ⊕ X) + XZ + XY + XZ ABC + ABCD + ABD
BC + ABCD + ABCD + ABCD

(X + Y)(XY) + ZXY + XZY (A + B ) (A + B) ( AB)

(A + AB) ((A + B + C) (C) ((A + B) x z+ xyz + x y
y z + x y z + xz + y

(A + AB) (A + B) + B
(X + Y) + (X ⊕ ( X ⊕ XY))

(X⊕(XY⊕(X⊕X)))

Asimple speed reducer is composed of 2 spur gears. the pinion gear has a pitch diameter of 0.75" and 36 teeth while the driven gear has a pitch diameter of 4.0" and 192 teeth. a)-what is the diametral pitch of each gear? b)-if an electric motor rotating ccw at 3000 rpm is coupled to the pinion, what is the rotational speed of the driven gear? c)-if the torque delivered to the pinion is 1 n-m, what is the torque on the driven gear? d)-what is the power transmitted by the gear train?