Intelligent Systems by Universal Teacher Publications

Formalized Symbolic Logics

Conjunctive & Disjunctive Normal Form

Q. Transform the following into Disjunctive Normal Form:
P à (^~(Q à R) (Dec. 02)

P à (^~(Q à R)
P à (^~(^~Q Ú R))
^~P Ú (^~(^~Q Ú R))
^~ [P & (^~Q Ú R)]
^~ [(P & ^~Q) Ú (P & R)]

Q. Transform the following into Conjunctive Normal Form:
i. Z à (^~(X à Y) (Dec. 01)
ii. (P Û Q) Ú R (June 01)

i. Z à (^~(X à Y)
Z à (^~(^~X Ú Y))
^~Z Ú (^~(^~X Ú Y))
^~Z Ú (X & ^~Y)
(^~Z Ú X) & (Z Ú ^~Y)]

ii. (P Û Q) Ú R
(P à Q) & (Q à P) Ú R
(^~P Ú Q) & (^~Q Ú P) Ú R
R Ú (^~P Ú Q) & (^~Q Ú P)
(R Ú ^~P Ú Q) & (R Ú ^~Q Ú P)