Discrete Mathematics 5

Discrete Mathematics Five

The use of the primary disjunction paradigm

1. To find the formula of the true assignment and false assignment value.

2. Determine the type of formula. It is a tautology, a contradiction or a satisfying formula.

3. Determine whether the two proposition formulas are equivalent.

Example: Use the main disjunctive paradigm of a formula to determine the type of formula described below:

If there are n propositional changes in formula A, the primary disjunction paradigm of a has s minima, that A has a true assignment of S, and 2n-s is a false value. If there are 2n into the true value is the tautology, there are 0 is the contradiction, the rest is to be satisfied.

Example: Determine whether the following two sets of formulas are equivalent:

Finally, it is an example to analyze and solve practical problems by using the main disjunctive paradigm.

Example: A scientific research institute should choose 1-2 students to study abroad from 3 key a,b,c. Due to the need for work, the following conditions shall be met when selected:

(1) If a goes, then C goes with it.

(2) If b goes, then C cannot go.

(3) If C does not go, then a or B can go.

What are the details of the program in question?

Solution: Set P: Send A To

Q: Send B to

R: Send C to

If a goes to C go with, meaning a to go to C, but c to a not necessarily go, that is

p	q	If a goes to C go
0	0	1
0	1	1
1	0	0
1	1	1

Only if the p is true q is false, so if a go to C go can be written as: P→q

So (2) can be written as Q→￢r, (3) can be written as ￢r→ (P∨Q)

Therefore, the following formula should be chosen to be true

(p→q) ∧ (q→￢r) ∧ (￢r→ (P∨Q))

There are 3 minimum items, so a total of three options are selected:

(1) A does not go to B not go to C.

(2) A does not go to B to go to C.

(3) A go to B not go to C.

How does the main disjunctive paradigm seek the main form of the collection?

Example: Using the main disjunctive paradigm of the formula to find the main model.

Discrete Mathematics 5