__PDNF__:

It stands for Principal Disjunctive Normal Form. It refers to the Sum of Products, i.e., SOP. For eg. : If P, Q, R are the variables then ** (P . Q’ . R) + (P’ . Q . R) + (P . Q . R’) ** is an example of an expression in PDNF. Here ‘+’ i.e. sum is the main operator.

You might be confused if there exists any difference between DNF (Disjunctive Normal Form) and PDNF (Principal Disjunctive Normal Form). The Key difference between PDNF and DNF is that in case of DNF, it is not necessary that the length of all the variables in the expression is same. For eg.:

**(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__:

It stands for Principal Conjunctive Normal Form. It refers to the Product of Sums, i.e., POS. For eg. : If P, Q, R are the variables then ** (P + Q’+ R).(P’+ Q + R).(P + Q + R’) ** is an example of an expression in PCNF. Here ‘.’ i.e. product is the main operator.

Here also, the Key difference between PCNF and CNF is that in case of CNF, it is not necessary that the length of all the variables in the expression is same . For eg.:

**(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 = .

Attention reader! Don’t stop learning now. Get hold of all the important CS Theory concepts for SDE interviews with the CS Theory Course at a student-friendly price and become industry ready.

## Recommended Posts:

- Discrete Mathematics | Types of Recurrence Relations - Set 2
- Discrete Mathematics | Representing Relations
- Discrete Mathematics | Hasse Diagrams
- Last Minute Notes – Discrete Mathematics
- Discrete Maths | Generating Functions-Introduction and Prerequisites
- Mathematics | Predicates and Quantifiers | Set 1
- Mathematics | Mean, Variance and Standard Deviation
- Mathematics | Sum of squares of even and odd natural numbers
- Mathematics | Eigen Values and Eigen Vectors
- Mathematics | Introduction and types of Relations
- Mathematics | Representations of Matrices and Graphs in Relations
- Mathematics | Covariance and Correlation
- Mathematics | Predicates and Quantifiers | Set 2
- Mathematics | Closure of Relations and Equivalence Relations
- Mathematics | Partial Orders and Lattices
- Mathematics | Graph Isomorphisms and Connectivity
- Mathematics | Planar Graphs and Graph Coloring
- Mathematics | Euler and Hamiltonian Paths
- Mathematics | PnC and Binomial Coefficients
- Mathematics | Limits, Continuity and Differentiability

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.