Answer
P^~Q^~R
See figure.
Work Step by Step
1. Use Theorem 2.1.1 to simplify the given expression:
(P^Q^R)v(P^~Q^R)v(P^~Q^~R)$\equiv$
(P^R^Q)v(P^R^~Q)v(P^~Q^~R)$\equiv$
(P^R)^(Qv~Q)v(P^~Q^~R)$\equiv$
(P^R)^(t)v(P^~Q^~R)$\equiv$
(P^R)v(P^~Q^~R)$\equiv$
(P^P^~Q^~R)v(R^P^~Q^~R)$\equiv$
(P^~Q^~R)v(c^P^~Q)$\equiv$
(P^~Q^~R)v(c)$\equiv$
P^~Q^~R
2. The above can be represented by a circuit of three gates as shown.
