PDNF and PCNF in Discrete Mathematics
PDNF:
(P . Q’ . R) + (P’ . Q . R) + (P . Q . R’)
- (P . Q’ . R) + (P’ . Q . R) + (P . Q) is an example of an expression in DNF but not in PDNF.
- (P . Q’ . R) + (P’ . Q . R) + (P . Q . R’) is an example of an expression which is both in PDNF and DNF.
PCNF:
(P + Q’+ R).(P’+ Q + R).(P + Q + R’)
- (P + Q’+ R).(P’+ Q + R).(P + Q) is an example of an expression in CNF but not in PCNF.
- (P + Q’+ R).(P’+ Q + R).(P + Q + R’) is an example of an expression which is both in PCNF and CNF.
Properties of PCNF and PDNF:
- Every PDNF or PCNF corresponds to a unique Boolean Expression and vice versa.
- If X and Y are two Boolean expressions then, X is equivalent to Y if and only if PDNF(X) = PDNF(Y) or PCNF(X) = PCNF(Y).
- For a Boolean Expression, if PCNF has m terms and PDNF has n terms, then the number of variables in such a Boolean expression = .
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