**(P ^ (P => Q)) => Q **named **Modus ponens **meaning affirms by affirming – affirming the antecedent/premise P

If the compound statement (P ^ (P => Q)) => Q is given and is true (it is always true) and P => Q is true then P must be true – therefore Q must be true (see truth table to follow the reasoning).

` P => Q (If P => Q is true then...)`

P (must be true)

therefore Q must be true.

In English:

P = today is Tuesday

Q = I will go to work

If today is Tuesday, then I will go to work.

Today is Tuesday.

Therefore, I will go to work.

In instances of modus ponens we assume as premises that p => q is true and p is true. Only one line of the truth table – the last – satisfies these two conditions. On this line, q is also true. Therefore, whenever p => q is true and p is true, q must also be true

3 no namers – logical implications

Hypothetical Syllogism – a logical implication

Disjunctive Syllogism – a logical implication

Simplification – a logical implication

Addition – a logical implication

Modus tollens – a logical implication

Modus ponens – a logical implication

Logical Implications

see Wikipedia