Modus Ponen & Chain Rule

 Premise:

A premise is a proposition on which an argument is based or from which a conclusion is drawn

Hypothetical Proposition:

 It is a proposition in the form:

       

            "If P, then Q"    ( Symbolically : P→Q )

 here,

            P is known as "Antecedent"

            Q is known as "Consequent"

Inference Rules:

In Propositional Logic, there are 2 Inference Rules drawn from a hypothetical proposition:

        ➤ Modus Ponen

        ➤ Modus Tollen

Modus Ponen:    It is a method of affirming the consequent. This inference rule (modus ponen) form resembles a syllogism with 2 premises and a conclusion:

                            If P, then Q     (Symbolically : P→Q )    ( Premise 1)
                            

                            P,                                                               ( Premise 2)
            therefore,

                            Q                                                               ( Conclusion)

we can understand it with this example:

                            "If you have an ATM card, then you can withdraw money from ATM machine"
     

                             You have an ATM card
                 therefore,

                             You can withdraw money from ATM machine.

Modus Tollen:    It is a method of denying the antecedent. It is an argument of the form:

                            If P, then Q     (Symbolically : P→Q )

                           ~Q,
           therefore,

                            ~P

we can understand it with following example:

                    "If you have an ATM card, then you can withdraw money from ATM machine"
     

                      You can not withdraw money from ATM machine
             therefore,

                      you do not have an ATM card.

Chain Rule:    It is hypothetical syllogism with a conditional for one or both of its premises.

we can express it algebrically as:

                        P→Q

                        Q→R

        therefore,

                        P→R

Let us understand it with this example:

                        "If I go to school daily, then I will be well educated"

                        "If I will be well educated, then I will get a good job"

from this we can conclude,

                        "If I go to school daily, then I will get a good job"

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Propositional Logic

Propositions are simple atomic sentences which are connected using logical connectives and propositional logic represents logic through propositions

A proposition can have true or False as its value.

This part will cover the propositions, their types and other related terms.

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