What is the conditional rule in propositional calculus and how is it used?

  • Thread starter evagelos
  • Start date
  • Tags
    Conditional
In summary, the conditional rule, also known as the deduction theorem, is an operator in propositional calculus where A => B is equivalent to ~A v B. It is commonly used in ordinary mathematical proofs, as it helps to express logical implications and conclusions. This rule is essential in mathematical logic and can be found in many mathematics books.
  • #1
evagelos
315
0
what is conditional rule,how is it used in:

1) propositional calculus

2) IN ordinary mathematical proofs ,examples will help
 
Physics news on Phys.org
  • #2
In propositional calculus, A => B is equivalent to ~A v B. It's just one more of those logic operators which can be expressed in others (or: be used to express all others in). But implication is an "intuitive" rule, in the sense that it indicates something logically following from something else.

In "ordinary" mathematical proofs, it is used all the time. Open any mathematics book and it will be full of statements like "if ..., then ...", "assuming ..., we can show ..." and "from ... it follows that ...".
 
  • #3
I AM sorry it was my mistake what i actually meant by conditional rule it was ;

the rule of conditional proof ,known as the DEDUCTION THEOREM in some books

thank you
 

1. What is a conditional rule?

A conditional rule is a statement or command that is only executed if a certain condition is met. It allows for the creation of logic and decision-making in programming and other scientific fields.

2. How is a conditional rule written?

A conditional rule is typically written in the form of an "if-then" statement. For example, "if this condition is true, then perform this action". The condition can be based on a variety of factors, such as values, user input, or other variables.

3. What is the purpose of a conditional rule?

The purpose of a conditional rule is to control the flow of a program or experiment based on certain conditions. It allows for more efficient and effective decision-making, as well as the ability to handle different scenarios and outcomes.

4. Can a conditional rule have multiple conditions?

Yes, a conditional rule can have multiple conditions. This is often referred to as "nested" conditions and allows for more complex logic and decision-making. Multiple conditions can also be combined using logical operators, such as "and" or "or".

5. What happens if the condition in a conditional rule is not met?

If the condition in a conditional rule is not met, the statement or command within the "if" block will not be executed. However, there may be alternative actions or commands within an "else" block that will be executed if the condition is not met.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
33
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
962
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
865
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
900
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
Back
Top