Teaching page of Shervine Amidi, Graduate Student at Stanford University.

This elimination rule is sometimes called “modus ponens”.

Modus Ponens or Law of Detachment Example: Let p be “It is snowing. .

Biconditional introduction (↔ Intro) P Q Q P P ↔ Q This rule is, effectively, a double use of → Intro.

Thus, Modus Ponens has the form of a valid argument.

. . P is true.

q 1, 2, modus ponens 4.

. P is true. In this case, we have written (modus ponens).

It can be summarized as "P implies Q. Thus, we say, for the above example, that the third line is derived from the earlier two lines using modus ponens.

In simboli la scriviamo cos X;X ! Y Y In questi episodio chiamer o S 0 il sistema assiomatico costituito dagli assiomi in A 1 e A 2 e dalla regola di inferenza Modus Ponens.

” “Therefore , I will study discrete math.

• If is a theorem (provable), –We can prove or. .

If antecedent = true, consequence = true. .

[3] It can be summarized as " P implies Q.
.
P is true.

P is true.

We already proved that modus ponens is sound, and now we have that it is complete (for Horn clauses).

. Therefore Q must also be true. , modus ponens) with the children as premises.

. s 3, 4, modus ponens 6. Notice that with one exception, the laws are paired in such a way that exchanging the symbols ∧, ∨, 1 and 0 for ∨, ∧, 0, and 1, respectively, in any law gives you a second law. ” “Therefore , I will study discrete math. .

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Definition 2. On the right-hand side of a rule, we often write the name of the rule.

In propositional logic, modus ponens ( / ˈmoʊdəs ˈpoʊnɛnz /; MP ), also known as modus ponendo ponens ( Latin for "method of putting by placing"), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference.

Similarly, if A→S is outside the scope of H, apply axiom 1, (A→S)→(H→(A→S)), and modus ponens to get H→(A→S).

p →s 1, 5, direct method of proof MSU/CSE 260 Fall 2009 15 Example: Contrapositive proof Prove hypothetical syllogism.

P is true.

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