Modus ponens is one of my favorite in the rules of inference. I submitted this A4 size poster to my prof in discrete math 1 subject.
In propositional logic, modus ponendo ponens (Latin for “the way that affirms by affirming”; generally abbreviated to MP or modus ponens) or implication elimination is a rule of inference. It can be summarized as “P implies Q and P is asserted to be true, so therefore Q must be true.”
The argument form has two premises (hypothesis). The first premise is the “if–then” or conditional claim, namely that P implies Q. The second premise is that P, the antecedent of the conditional claim, is true. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be true as well. In artificial intelligence, modus ponens is often called forward chaining.
Statement: If I love you so, then I will make it up for you. I love you. Therefore, I will make it up for you.
Let P = If I love you so,
and Q = then I will make it up for you.
Let P = I love you.
∴ = I will make it up for you.
Justification via truth table
p | q | p → q
T | T | T
T | F | F
F | T | T
F | F | T