Symbolic Logic - Assignment Example

Modus Ponens

Modus ponens is a rule of inference where if one proposition implies the second proposition and the first proposition is true, then the second is also true. Example of argument:

If it is raining, I’ll not go to school. It is raining; therefore, I’ll not go to school.

It is raining (P)                                                           It is not raining (-p)

I’ll go to school (Q)                                                   I’ll not go to school (-Q)                                    Therefore (…)

Symbol:

If P → -Q, p … -Q

Modus Tollens

It is a rule of inference where if a proposition implies the second and the second proposition is not true, then the first proposition cannot be true.

If a motion detector detects any movement, it will turn on the security alarm.

The security alarm wasn’t turned on.

Therefore, the motion detector didn’t detect any movement.

Motion detector detected movement (P)        Motion detector didn’t detect any movement (-P)

A security alarm is on (Q)                                         Security alarm is off (-Q)

Symbol

P→ Q, -Q … -P